87156
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0\) are respectively
1 2,4
2 2,3
3 2,2
4 3,4
5 4,3
Explanation:
(C) : Given that, \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0 \Rightarrow \sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{\frac{3}{2}}}=-\frac{d^{2} y}{d x^{2}}\) On squaring on both side- \(x^{2}+\left[\frac{d y}{d x}\right]^{3 / 2}=\left[-\frac{d^{2} y}{d x^{2}}\right]^{2} \Rightarrow x^{2}+\left[\frac{d y}{d x}\right]^{\frac{3}{2}}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) \(\therefore \quad\) Order \(=2\) and degree \(=2\)
Kerala CEE-2020
Differential Equation
87157
The degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}} \text { is }\)
1 1
2 2
3 3
4 4
5 5
Explanation:
(B) : Given that, \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}}\) On squaring both sides, we get- \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) So, the degree of differential equation is 2 .
Kerala CEE-2019
Differential Equation
87160
The differential equation representing the family of curves \(y^{2}=a(a x+b)\), where \(a\) and \(b\) are arbitrary constants, is of
1 order 1, degree 1
2 order 1, degree 3
3 order 2, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(E) : Given that, \(y^{2}=a(a x+b)\) \(y^{2}=a^{2} x+a b\) On differentiating with respect to \(\mathrm{x}\), we get- \(2 y \frac{d y}{d x}=a^{2} \Rightarrow y \frac{d y}{d x}=\frac{a^{2}}{2}\) \(y \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x} \cdot \frac{d y}{d x}=0\) Hence, order and degree of the given equation is 2 and 1 respectively.
Kerala CEE-2016
Differential Equation
87161
The order and degree of the differential equation \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\left(\frac{d^{3} y}{d x^{3}}\right) \text { are respectively. }\)
1 2 and 2
2 2 and 1
3 3 and 2
4 3 and 3
5 2 and 4
Explanation:
(C) : Given that the differential equation- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3} y}{d x^{3}}\) On squaring both sides, we get- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}\) Hence, order is 3 and degree is 2.
Kerala CEE-2015
Differential Equation
87083
If ' \(m\) ' and ' \(n\) ' are the order and degree of the differential equation \(\left(y^{\prime \prime}\right)^{5}+4 \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x \text {, then }\)
87156
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0\) are respectively
1 2,4
2 2,3
3 2,2
4 3,4
5 4,3
Explanation:
(C) : Given that, \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0 \Rightarrow \sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{\frac{3}{2}}}=-\frac{d^{2} y}{d x^{2}}\) On squaring on both side- \(x^{2}+\left[\frac{d y}{d x}\right]^{3 / 2}=\left[-\frac{d^{2} y}{d x^{2}}\right]^{2} \Rightarrow x^{2}+\left[\frac{d y}{d x}\right]^{\frac{3}{2}}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) \(\therefore \quad\) Order \(=2\) and degree \(=2\)
Kerala CEE-2020
Differential Equation
87157
The degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}} \text { is }\)
1 1
2 2
3 3
4 4
5 5
Explanation:
(B) : Given that, \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}}\) On squaring both sides, we get- \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) So, the degree of differential equation is 2 .
Kerala CEE-2019
Differential Equation
87160
The differential equation representing the family of curves \(y^{2}=a(a x+b)\), where \(a\) and \(b\) are arbitrary constants, is of
1 order 1, degree 1
2 order 1, degree 3
3 order 2, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(E) : Given that, \(y^{2}=a(a x+b)\) \(y^{2}=a^{2} x+a b\) On differentiating with respect to \(\mathrm{x}\), we get- \(2 y \frac{d y}{d x}=a^{2} \Rightarrow y \frac{d y}{d x}=\frac{a^{2}}{2}\) \(y \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x} \cdot \frac{d y}{d x}=0\) Hence, order and degree of the given equation is 2 and 1 respectively.
Kerala CEE-2016
Differential Equation
87161
The order and degree of the differential equation \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\left(\frac{d^{3} y}{d x^{3}}\right) \text { are respectively. }\)
1 2 and 2
2 2 and 1
3 3 and 2
4 3 and 3
5 2 and 4
Explanation:
(C) : Given that the differential equation- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3} y}{d x^{3}}\) On squaring both sides, we get- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}\) Hence, order is 3 and degree is 2.
Kerala CEE-2015
Differential Equation
87083
If ' \(m\) ' and ' \(n\) ' are the order and degree of the differential equation \(\left(y^{\prime \prime}\right)^{5}+4 \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x \text {, then }\)
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Differential Equation
87156
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0\) are respectively
1 2,4
2 2,3
3 2,2
4 3,4
5 4,3
Explanation:
(C) : Given that, \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0 \Rightarrow \sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{\frac{3}{2}}}=-\frac{d^{2} y}{d x^{2}}\) On squaring on both side- \(x^{2}+\left[\frac{d y}{d x}\right]^{3 / 2}=\left[-\frac{d^{2} y}{d x^{2}}\right]^{2} \Rightarrow x^{2}+\left[\frac{d y}{d x}\right]^{\frac{3}{2}}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) \(\therefore \quad\) Order \(=2\) and degree \(=2\)
Kerala CEE-2020
Differential Equation
87157
The degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}} \text { is }\)
1 1
2 2
3 3
4 4
5 5
Explanation:
(B) : Given that, \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}}\) On squaring both sides, we get- \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) So, the degree of differential equation is 2 .
Kerala CEE-2019
Differential Equation
87160
The differential equation representing the family of curves \(y^{2}=a(a x+b)\), where \(a\) and \(b\) are arbitrary constants, is of
1 order 1, degree 1
2 order 1, degree 3
3 order 2, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(E) : Given that, \(y^{2}=a(a x+b)\) \(y^{2}=a^{2} x+a b\) On differentiating with respect to \(\mathrm{x}\), we get- \(2 y \frac{d y}{d x}=a^{2} \Rightarrow y \frac{d y}{d x}=\frac{a^{2}}{2}\) \(y \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x} \cdot \frac{d y}{d x}=0\) Hence, order and degree of the given equation is 2 and 1 respectively.
Kerala CEE-2016
Differential Equation
87161
The order and degree of the differential equation \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\left(\frac{d^{3} y}{d x^{3}}\right) \text { are respectively. }\)
1 2 and 2
2 2 and 1
3 3 and 2
4 3 and 3
5 2 and 4
Explanation:
(C) : Given that the differential equation- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3} y}{d x^{3}}\) On squaring both sides, we get- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}\) Hence, order is 3 and degree is 2.
Kerala CEE-2015
Differential Equation
87083
If ' \(m\) ' and ' \(n\) ' are the order and degree of the differential equation \(\left(y^{\prime \prime}\right)^{5}+4 \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x \text {, then }\)
87156
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0\) are respectively
1 2,4
2 2,3
3 2,2
4 3,4
5 4,3
Explanation:
(C) : Given that, \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0 \Rightarrow \sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{\frac{3}{2}}}=-\frac{d^{2} y}{d x^{2}}\) On squaring on both side- \(x^{2}+\left[\frac{d y}{d x}\right]^{3 / 2}=\left[-\frac{d^{2} y}{d x^{2}}\right]^{2} \Rightarrow x^{2}+\left[\frac{d y}{d x}\right]^{\frac{3}{2}}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) \(\therefore \quad\) Order \(=2\) and degree \(=2\)
Kerala CEE-2020
Differential Equation
87157
The degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}} \text { is }\)
1 1
2 2
3 3
4 4
5 5
Explanation:
(B) : Given that, \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}}\) On squaring both sides, we get- \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) So, the degree of differential equation is 2 .
Kerala CEE-2019
Differential Equation
87160
The differential equation representing the family of curves \(y^{2}=a(a x+b)\), where \(a\) and \(b\) are arbitrary constants, is of
1 order 1, degree 1
2 order 1, degree 3
3 order 2, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(E) : Given that, \(y^{2}=a(a x+b)\) \(y^{2}=a^{2} x+a b\) On differentiating with respect to \(\mathrm{x}\), we get- \(2 y \frac{d y}{d x}=a^{2} \Rightarrow y \frac{d y}{d x}=\frac{a^{2}}{2}\) \(y \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x} \cdot \frac{d y}{d x}=0\) Hence, order and degree of the given equation is 2 and 1 respectively.
Kerala CEE-2016
Differential Equation
87161
The order and degree of the differential equation \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\left(\frac{d^{3} y}{d x^{3}}\right) \text { are respectively. }\)
1 2 and 2
2 2 and 1
3 3 and 2
4 3 and 3
5 2 and 4
Explanation:
(C) : Given that the differential equation- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3} y}{d x^{3}}\) On squaring both sides, we get- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}\) Hence, order is 3 and degree is 2.
Kerala CEE-2015
Differential Equation
87083
If ' \(m\) ' and ' \(n\) ' are the order and degree of the differential equation \(\left(y^{\prime \prime}\right)^{5}+4 \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x \text {, then }\)
87156
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0\) are respectively
1 2,4
2 2,3
3 2,2
4 3,4
5 4,3
Explanation:
(C) : Given that, \(\frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{3 / 2}}=0 \Rightarrow \sqrt{x^{2}+\left(\frac{d y}{d x}\right)^{\frac{3}{2}}}=-\frac{d^{2} y}{d x^{2}}\) On squaring on both side- \(x^{2}+\left[\frac{d y}{d x}\right]^{3 / 2}=\left[-\frac{d^{2} y}{d x^{2}}\right]^{2} \Rightarrow x^{2}+\left[\frac{d y}{d x}\right]^{\frac{3}{2}}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) \(\therefore \quad\) Order \(=2\) and degree \(=2\)
Kerala CEE-2020
Differential Equation
87157
The degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}} \text { is }\)
1 1
2 2
3 3
4 4
5 5
Explanation:
(B) : Given that, \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=1 \frac{d^{2} y}{d x^{2}}\) On squaring both sides, we get- \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left[\frac{d^{2} y}{d x^{2}}\right]^{2}\) So, the degree of differential equation is 2 .
Kerala CEE-2019
Differential Equation
87160
The differential equation representing the family of curves \(y^{2}=a(a x+b)\), where \(a\) and \(b\) are arbitrary constants, is of
1 order 1, degree 1
2 order 1, degree 3
3 order 2, degree 3
4 order 1, degree 4
5 order 2, degree 1
Explanation:
(E) : Given that, \(y^{2}=a(a x+b)\) \(y^{2}=a^{2} x+a b\) On differentiating with respect to \(\mathrm{x}\), we get- \(2 y \frac{d y}{d x}=a^{2} \Rightarrow y \frac{d y}{d x}=\frac{a^{2}}{2}\) \(y \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x} \cdot \frac{d y}{d x}=0\) Hence, order and degree of the given equation is 2 and 1 respectively.
Kerala CEE-2016
Differential Equation
87161
The order and degree of the differential equation \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\left(\frac{d^{3} y}{d x^{3}}\right) \text { are respectively. }\)
1 2 and 2
2 2 and 1
3 3 and 2
4 3 and 3
5 2 and 4
Explanation:
(C) : Given that the differential equation- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3} y}{d x^{3}}\) On squaring both sides, we get- \(\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}\) Hence, order is 3 and degree is 2.
Kerala CEE-2015
Differential Equation
87083
If ' \(m\) ' and ' \(n\) ' are the order and degree of the differential equation \(\left(y^{\prime \prime}\right)^{5}+4 \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x \text {, then }\)