87110
\(\frac{d^{3} y}{d x^{3}}+2\left[1+\frac{d^{2} y}{d x^{2}}\right]=1\) has degree and order as:
1 3,1
2 3,2
3 1,3
4 2,3
Explanation:
(C) : Given, the differential equation \(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}+2\left[1+\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]=1\) Hence, order is 3 and degree is 1
JCECE-2004
Differential Equation
87119
The order and degree of the differential equation \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) are
1 1,4
2 3,4
3 2,4
4 3,2
Explanation:
(D) : We have the following differential equation, \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) Hence, Order \(=3\) Degree \(=2\)
CG PET- 2012
Differential Equation
87129
If \(p\) and \(q\) are the order and degree of the differential equation \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\), then
1 \(\mathrm{p}\lt \mathrm{q}\)
2 \(p=q\)
3 \(p>q\)
4 none of these
Explanation:
(A) : Given, \(\mathrm{p}\) and \(\mathrm{q}\) are the order and degree of the differential equation, \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\) It shows that order is 2 and degree is 3. Hence \(\mathrm{p}\lt \mathrm{q}\)
AMU-2016
Differential Equation
87149
The order and degree of the differential equation \(\quad \frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\), are respectively.
1 3,4
2 2,2
3 3,2
4 3,3
Explanation:
(D) : Given differential equation, \(\frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\) \(\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=-\left(\frac{d^{2} y}{d x^{2}}+y\right) \Rightarrow\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3}=\left(\frac{d^{2} y}{d x^{2}}+y\right)^{2}\) Clearly, order and degree is 3 and 3 respectively.
NEET Test Series from KOTA - 10 Papers In MS WORD
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Differential Equation
87110
\(\frac{d^{3} y}{d x^{3}}+2\left[1+\frac{d^{2} y}{d x^{2}}\right]=1\) has degree and order as:
1 3,1
2 3,2
3 1,3
4 2,3
Explanation:
(C) : Given, the differential equation \(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}+2\left[1+\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]=1\) Hence, order is 3 and degree is 1
JCECE-2004
Differential Equation
87119
The order and degree of the differential equation \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) are
1 1,4
2 3,4
3 2,4
4 3,2
Explanation:
(D) : We have the following differential equation, \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) Hence, Order \(=3\) Degree \(=2\)
CG PET- 2012
Differential Equation
87129
If \(p\) and \(q\) are the order and degree of the differential equation \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\), then
1 \(\mathrm{p}\lt \mathrm{q}\)
2 \(p=q\)
3 \(p>q\)
4 none of these
Explanation:
(A) : Given, \(\mathrm{p}\) and \(\mathrm{q}\) are the order and degree of the differential equation, \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\) It shows that order is 2 and degree is 3. Hence \(\mathrm{p}\lt \mathrm{q}\)
AMU-2016
Differential Equation
87149
The order and degree of the differential equation \(\quad \frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\), are respectively.
1 3,4
2 2,2
3 3,2
4 3,3
Explanation:
(D) : Given differential equation, \(\frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\) \(\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=-\left(\frac{d^{2} y}{d x^{2}}+y\right) \Rightarrow\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3}=\left(\frac{d^{2} y}{d x^{2}}+y\right)^{2}\) Clearly, order and degree is 3 and 3 respectively.
87110
\(\frac{d^{3} y}{d x^{3}}+2\left[1+\frac{d^{2} y}{d x^{2}}\right]=1\) has degree and order as:
1 3,1
2 3,2
3 1,3
4 2,3
Explanation:
(C) : Given, the differential equation \(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}+2\left[1+\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]=1\) Hence, order is 3 and degree is 1
JCECE-2004
Differential Equation
87119
The order and degree of the differential equation \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) are
1 1,4
2 3,4
3 2,4
4 3,2
Explanation:
(D) : We have the following differential equation, \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) Hence, Order \(=3\) Degree \(=2\)
CG PET- 2012
Differential Equation
87129
If \(p\) and \(q\) are the order and degree of the differential equation \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\), then
1 \(\mathrm{p}\lt \mathrm{q}\)
2 \(p=q\)
3 \(p>q\)
4 none of these
Explanation:
(A) : Given, \(\mathrm{p}\) and \(\mathrm{q}\) are the order and degree of the differential equation, \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\) It shows that order is 2 and degree is 3. Hence \(\mathrm{p}\lt \mathrm{q}\)
AMU-2016
Differential Equation
87149
The order and degree of the differential equation \(\quad \frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\), are respectively.
1 3,4
2 2,2
3 3,2
4 3,3
Explanation:
(D) : Given differential equation, \(\frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\) \(\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=-\left(\frac{d^{2} y}{d x^{2}}+y\right) \Rightarrow\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3}=\left(\frac{d^{2} y}{d x^{2}}+y\right)^{2}\) Clearly, order and degree is 3 and 3 respectively.
87110
\(\frac{d^{3} y}{d x^{3}}+2\left[1+\frac{d^{2} y}{d x^{2}}\right]=1\) has degree and order as:
1 3,1
2 3,2
3 1,3
4 2,3
Explanation:
(C) : Given, the differential equation \(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}+2\left[1+\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]=1\) Hence, order is 3 and degree is 1
JCECE-2004
Differential Equation
87119
The order and degree of the differential equation \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) are
1 1,4
2 3,4
3 2,4
4 3,2
Explanation:
(D) : We have the following differential equation, \(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}-3 \frac{d^{2} y}{d x^{2}}+2\left(\frac{d y}{d x}\right)^{4}=y^{4}\) Hence, Order \(=3\) Degree \(=2\)
CG PET- 2012
Differential Equation
87129
If \(p\) and \(q\) are the order and degree of the differential equation \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\), then
1 \(\mathrm{p}\lt \mathrm{q}\)
2 \(p=q\)
3 \(p>q\)
4 none of these
Explanation:
(A) : Given, \(\mathrm{p}\) and \(\mathrm{q}\) are the order and degree of the differential equation, \(y \frac{d y}{d x}+x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+x y=\cos x\) It shows that order is 2 and degree is 3. Hence \(\mathrm{p}\lt \mathrm{q}\)
AMU-2016
Differential Equation
87149
The order and degree of the differential equation \(\quad \frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\), are respectively.
1 3,4
2 2,2
3 3,2
4 3,3
Explanation:
(D) : Given differential equation, \(\frac{d^{2} y}{d x^{2}}+y+\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=0\) \(\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=-\left(\frac{d^{2} y}{d x^{2}}+y\right) \Rightarrow\left(\frac{d y}{d x}-\frac{d^{3} y}{d x^{3}}\right)^{3}=\left(\frac{d^{2} y}{d x^{2}}+y\right)^{2}\) Clearly, order and degree is 3 and 3 respectively.
