87081
The order of differential equation of all circles of given radius ' \(a\) ' is
1 2
2 3
3 4
4 1
Explanation:
(A) : Given that, a circle having radius ' \(a\) ' the general equation of circles \((r-h)^{2}+(y-k)^{2}=a^{2}\) It has two arbitrary constant h, and k, therefore the order of the given differential equation is 2 .
Karnataka CET-2015
Differential Equation
87138
The degree of the differential equation \(\left[5+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=x^{5}\left[\frac{d^{2} y}{d x^{2}}\right] \text { is }\)
87152
For the differential \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) has the order and degree respectively.
1 2 and 3
2 2 and 6
3 2 and 1
4 2 and 2
Explanation:
(A) : Given that, the differential equation- \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) Here, \(\left[1-\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{5}=8^{3}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{3}\) \(\therefore\) Order \(=2\) and degree \(=3\)
MHT CET-2022
Differential Equation
87153
The order and degree of the differential equation \(\sqrt[3]{\frac{d^{2} y}{d^{2}}}=\sqrt{\frac{d y}{d x}}\) are respectively
1 3,3
2 1,3
3 2,3
4 2, 2
Explanation:
(D) : Given, \(\sqrt[3]{\frac{d^{2} y}{d x^{2}}}=\sqrt{\frac{d y}{d x}} \Rightarrow\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left(\frac{d y}{d x}\right)^{3}\) or, \(\quad\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=0\) Clearly, order is 2 and degree of the differential equation is 2.
MHT CET-2021
Differential Equation
87155
If \(m\) is order and \(n\) is degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
1 \(\mathrm{m}=3, \mathrm{n}=5\)
2 \(\mathrm{m}=3, \mathrm{n}=3\)
3 \(\mathrm{m}=3, \mathrm{n}=2\)
4 \(\mathrm{m}=3, \mathrm{n}=1\)
Explanation:
(C) : The given differential equation can be written as- \(\left(\frac{d^{3} y}{d x^{3}}\right) \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=\left(x^{2}-1\right) \cdot\left(\frac{d^{3} y}{d^{3}}\right)\) \(\therefore\) The order of the differential equation is 3 and degree is 2 . Hence, \(\mathrm{m}=3, \mathrm{n}=2\)
87081
The order of differential equation of all circles of given radius ' \(a\) ' is
1 2
2 3
3 4
4 1
Explanation:
(A) : Given that, a circle having radius ' \(a\) ' the general equation of circles \((r-h)^{2}+(y-k)^{2}=a^{2}\) It has two arbitrary constant h, and k, therefore the order of the given differential equation is 2 .
Karnataka CET-2015
Differential Equation
87138
The degree of the differential equation \(\left[5+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=x^{5}\left[\frac{d^{2} y}{d x^{2}}\right] \text { is }\)
87152
For the differential \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) has the order and degree respectively.
1 2 and 3
2 2 and 6
3 2 and 1
4 2 and 2
Explanation:
(A) : Given that, the differential equation- \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) Here, \(\left[1-\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{5}=8^{3}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{3}\) \(\therefore\) Order \(=2\) and degree \(=3\)
MHT CET-2022
Differential Equation
87153
The order and degree of the differential equation \(\sqrt[3]{\frac{d^{2} y}{d^{2}}}=\sqrt{\frac{d y}{d x}}\) are respectively
1 3,3
2 1,3
3 2,3
4 2, 2
Explanation:
(D) : Given, \(\sqrt[3]{\frac{d^{2} y}{d x^{2}}}=\sqrt{\frac{d y}{d x}} \Rightarrow\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left(\frac{d y}{d x}\right)^{3}\) or, \(\quad\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=0\) Clearly, order is 2 and degree of the differential equation is 2.
MHT CET-2021
Differential Equation
87155
If \(m\) is order and \(n\) is degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
1 \(\mathrm{m}=3, \mathrm{n}=5\)
2 \(\mathrm{m}=3, \mathrm{n}=3\)
3 \(\mathrm{m}=3, \mathrm{n}=2\)
4 \(\mathrm{m}=3, \mathrm{n}=1\)
Explanation:
(C) : The given differential equation can be written as- \(\left(\frac{d^{3} y}{d x^{3}}\right) \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=\left(x^{2}-1\right) \cdot\left(\frac{d^{3} y}{d^{3}}\right)\) \(\therefore\) The order of the differential equation is 3 and degree is 2 . Hence, \(\mathrm{m}=3, \mathrm{n}=2\)
87081
The order of differential equation of all circles of given radius ' \(a\) ' is
1 2
2 3
3 4
4 1
Explanation:
(A) : Given that, a circle having radius ' \(a\) ' the general equation of circles \((r-h)^{2}+(y-k)^{2}=a^{2}\) It has two arbitrary constant h, and k, therefore the order of the given differential equation is 2 .
Karnataka CET-2015
Differential Equation
87138
The degree of the differential equation \(\left[5+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=x^{5}\left[\frac{d^{2} y}{d x^{2}}\right] \text { is }\)
87152
For the differential \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) has the order and degree respectively.
1 2 and 3
2 2 and 6
3 2 and 1
4 2 and 2
Explanation:
(A) : Given that, the differential equation- \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) Here, \(\left[1-\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{5}=8^{3}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{3}\) \(\therefore\) Order \(=2\) and degree \(=3\)
MHT CET-2022
Differential Equation
87153
The order and degree of the differential equation \(\sqrt[3]{\frac{d^{2} y}{d^{2}}}=\sqrt{\frac{d y}{d x}}\) are respectively
1 3,3
2 1,3
3 2,3
4 2, 2
Explanation:
(D) : Given, \(\sqrt[3]{\frac{d^{2} y}{d x^{2}}}=\sqrt{\frac{d y}{d x}} \Rightarrow\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left(\frac{d y}{d x}\right)^{3}\) or, \(\quad\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=0\) Clearly, order is 2 and degree of the differential equation is 2.
MHT CET-2021
Differential Equation
87155
If \(m\) is order and \(n\) is degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
1 \(\mathrm{m}=3, \mathrm{n}=5\)
2 \(\mathrm{m}=3, \mathrm{n}=3\)
3 \(\mathrm{m}=3, \mathrm{n}=2\)
4 \(\mathrm{m}=3, \mathrm{n}=1\)
Explanation:
(C) : The given differential equation can be written as- \(\left(\frac{d^{3} y}{d x^{3}}\right) \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=\left(x^{2}-1\right) \cdot\left(\frac{d^{3} y}{d^{3}}\right)\) \(\therefore\) The order of the differential equation is 3 and degree is 2 . Hence, \(\mathrm{m}=3, \mathrm{n}=2\)
87081
The order of differential equation of all circles of given radius ' \(a\) ' is
1 2
2 3
3 4
4 1
Explanation:
(A) : Given that, a circle having radius ' \(a\) ' the general equation of circles \((r-h)^{2}+(y-k)^{2}=a^{2}\) It has two arbitrary constant h, and k, therefore the order of the given differential equation is 2 .
Karnataka CET-2015
Differential Equation
87138
The degree of the differential equation \(\left[5+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=x^{5}\left[\frac{d^{2} y}{d x^{2}}\right] \text { is }\)
87152
For the differential \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) has the order and degree respectively.
1 2 and 3
2 2 and 6
3 2 and 1
4 2 and 2
Explanation:
(A) : Given that, the differential equation- \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) Here, \(\left[1-\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{5}=8^{3}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{3}\) \(\therefore\) Order \(=2\) and degree \(=3\)
MHT CET-2022
Differential Equation
87153
The order and degree of the differential equation \(\sqrt[3]{\frac{d^{2} y}{d^{2}}}=\sqrt{\frac{d y}{d x}}\) are respectively
1 3,3
2 1,3
3 2,3
4 2, 2
Explanation:
(D) : Given, \(\sqrt[3]{\frac{d^{2} y}{d x^{2}}}=\sqrt{\frac{d y}{d x}} \Rightarrow\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left(\frac{d y}{d x}\right)^{3}\) or, \(\quad\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=0\) Clearly, order is 2 and degree of the differential equation is 2.
MHT CET-2021
Differential Equation
87155
If \(m\) is order and \(n\) is degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
1 \(\mathrm{m}=3, \mathrm{n}=5\)
2 \(\mathrm{m}=3, \mathrm{n}=3\)
3 \(\mathrm{m}=3, \mathrm{n}=2\)
4 \(\mathrm{m}=3, \mathrm{n}=1\)
Explanation:
(C) : The given differential equation can be written as- \(\left(\frac{d^{3} y}{d x^{3}}\right) \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=\left(x^{2}-1\right) \cdot\left(\frac{d^{3} y}{d^{3}}\right)\) \(\therefore\) The order of the differential equation is 3 and degree is 2 . Hence, \(\mathrm{m}=3, \mathrm{n}=2\)
87081
The order of differential equation of all circles of given radius ' \(a\) ' is
1 2
2 3
3 4
4 1
Explanation:
(A) : Given that, a circle having radius ' \(a\) ' the general equation of circles \((r-h)^{2}+(y-k)^{2}=a^{2}\) It has two arbitrary constant h, and k, therefore the order of the given differential equation is 2 .
Karnataka CET-2015
Differential Equation
87138
The degree of the differential equation \(\left[5+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=x^{5}\left[\frac{d^{2} y}{d x^{2}}\right] \text { is }\)
87152
For the differential \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) has the order and degree respectively.
1 2 and 3
2 2 and 6
3 2 and 1
4 2 and 2
Explanation:
(A) : Given that, the differential equation- \(\left[1-\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{5}{3}}=8 \frac{d^{2} y}{d x^{2}}\) Here, \(\left[1-\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{5}=8^{3}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{3}\) \(\therefore\) Order \(=2\) and degree \(=3\)
MHT CET-2022
Differential Equation
87153
The order and degree of the differential equation \(\sqrt[3]{\frac{d^{2} y}{d^{2}}}=\sqrt{\frac{d y}{d x}}\) are respectively
1 3,3
2 1,3
3 2,3
4 2, 2
Explanation:
(D) : Given, \(\sqrt[3]{\frac{d^{2} y}{d x^{2}}}=\sqrt{\frac{d y}{d x}} \Rightarrow\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left(\frac{d y}{d x}\right)^{3}\) or, \(\quad\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=0\) Clearly, order is 2 and degree of the differential equation is 2.
MHT CET-2021
Differential Equation
87155
If \(m\) is order and \(n\) is degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
1 \(\mathrm{m}=3, \mathrm{n}=5\)
2 \(\mathrm{m}=3, \mathrm{n}=3\)
3 \(\mathrm{m}=3, \mathrm{n}=2\)
4 \(\mathrm{m}=3, \mathrm{n}=1\)
Explanation:
(C) : The given differential equation can be written as- \(\left(\frac{d^{3} y}{d x^{3}}\right) \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=\left(x^{2}-1\right) \cdot\left(\frac{d^{3} y}{d^{3}}\right)\) \(\therefore\) The order of the differential equation is 3 and degree is 2 . Hence, \(\mathrm{m}=3, \mathrm{n}=2\)
