87096
The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) are equal to
1 \(\left(1, \frac{2}{3}\right)\)
2 \((3,1)\)
3 \((3,3)\)
4 \((1,2)\)
Explanation:
(C) :Given, differential equation. \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) Cubic on both sides, \(\left(1+3 \frac{d y}{d x}\right)^{2}=64\left(\frac{d^{3} y}{d x^{3}}\right)^{3}\) Hence, order and degree of the differential equation are 3 and 3 respectively.
CG PET-2018]**# / SRM JEEE-2016
Differential Equation
87098
The second order derivative of \(\frac{e^{x}+1}{e^{x}}\) is
1 \(e^{x}\)
2 \(\frac{1}{\mathrm{e}^{\mathrm{x}}}\)
3 \(\frac{e^{x}-1}{e^{x}}\)
4 \(e^{x}+\frac{1}{e^{x}}\)
Explanation:
(B) : Given \(y=\frac{e^{x}+1}{e^{x}}\) \(y=\frac{e^{x}}{e^{x}}+\frac{1}{e^{x}}\) \(\mathrm{y}=1+\frac{1}{\mathrm{e}^{\mathrm{x}}}\) Differentiating w.r.t. \(x\), we get - \(\frac{\mathrm{dy}}{\mathrm{dx}}=0+\left(-\mathrm{e}^{-\mathrm{x}}\right)\) Again differentiating w.r.t. \(x\), we get - \(\frac{d^{2} y}{d x^{2}}=-1(-1) e^{-x}=e^{-x}\) \(\frac{d^{2} y}{d x^{2}}=\frac{1}{e^{x}}\)
MHT CET-2004
Differential Equation
87099
The product of the degree and order of the D.E. \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) is
1 4
2 6
3 2
4 3
Explanation:
(A) : Given differential equation is \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) So, order \(=2\) and degree \(=2\) \(\therefore\) Product of the degree and order is, \(=2 \times 2=4\)
COMEDK-2015
Differential Equation
87101
The order and degree of the differential equation whose solution is \(\mathbf{y}=\mathbf{c x}+\mathbf{c}^{2}-3 \mathbf{c}^{3 / 2}+2\), where \(\mathbf{c}\) is a parameter, is
1 order \(=4\), degree \(=4\)
2 order \(=4\), degree \(=1\)
3 order \(=1\), degree \(=4\)
4 None of these
Explanation:
(C) : We have, \(y=c x+c^{2}-3 c^{3 / 2}+2 \tag{i}\) Differentiating both side with respect to \(\mathrm{x}\), we have \(\frac{d y}{d x}=c\) Putting this value of \(c\) in equation (i), we have \(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}-3\left(\frac{d y}{d x}\right)^{3 / 2}+2\) \(y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2=-3\left(\frac{d y}{d x}\right)^{3 / 2}\) Squaring both side, we have- \(\left[y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2\right]^{2}=9\left(\frac{d y}{d x}\right)^{3}\) So, order is 1 and degree is 4
NEET Test Series from KOTA - 10 Papers In MS WORD
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Differential Equation
87096
The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) are equal to
1 \(\left(1, \frac{2}{3}\right)\)
2 \((3,1)\)
3 \((3,3)\)
4 \((1,2)\)
Explanation:
(C) :Given, differential equation. \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) Cubic on both sides, \(\left(1+3 \frac{d y}{d x}\right)^{2}=64\left(\frac{d^{3} y}{d x^{3}}\right)^{3}\) Hence, order and degree of the differential equation are 3 and 3 respectively.
CG PET-2018]**# / SRM JEEE-2016
Differential Equation
87098
The second order derivative of \(\frac{e^{x}+1}{e^{x}}\) is
1 \(e^{x}\)
2 \(\frac{1}{\mathrm{e}^{\mathrm{x}}}\)
3 \(\frac{e^{x}-1}{e^{x}}\)
4 \(e^{x}+\frac{1}{e^{x}}\)
Explanation:
(B) : Given \(y=\frac{e^{x}+1}{e^{x}}\) \(y=\frac{e^{x}}{e^{x}}+\frac{1}{e^{x}}\) \(\mathrm{y}=1+\frac{1}{\mathrm{e}^{\mathrm{x}}}\) Differentiating w.r.t. \(x\), we get - \(\frac{\mathrm{dy}}{\mathrm{dx}}=0+\left(-\mathrm{e}^{-\mathrm{x}}\right)\) Again differentiating w.r.t. \(x\), we get - \(\frac{d^{2} y}{d x^{2}}=-1(-1) e^{-x}=e^{-x}\) \(\frac{d^{2} y}{d x^{2}}=\frac{1}{e^{x}}\)
MHT CET-2004
Differential Equation
87099
The product of the degree and order of the D.E. \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) is
1 4
2 6
3 2
4 3
Explanation:
(A) : Given differential equation is \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) So, order \(=2\) and degree \(=2\) \(\therefore\) Product of the degree and order is, \(=2 \times 2=4\)
COMEDK-2015
Differential Equation
87101
The order and degree of the differential equation whose solution is \(\mathbf{y}=\mathbf{c x}+\mathbf{c}^{2}-3 \mathbf{c}^{3 / 2}+2\), where \(\mathbf{c}\) is a parameter, is
1 order \(=4\), degree \(=4\)
2 order \(=4\), degree \(=1\)
3 order \(=1\), degree \(=4\)
4 None of these
Explanation:
(C) : We have, \(y=c x+c^{2}-3 c^{3 / 2}+2 \tag{i}\) Differentiating both side with respect to \(\mathrm{x}\), we have \(\frac{d y}{d x}=c\) Putting this value of \(c\) in equation (i), we have \(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}-3\left(\frac{d y}{d x}\right)^{3 / 2}+2\) \(y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2=-3\left(\frac{d y}{d x}\right)^{3 / 2}\) Squaring both side, we have- \(\left[y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2\right]^{2}=9\left(\frac{d y}{d x}\right)^{3}\) So, order is 1 and degree is 4
87096
The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) are equal to
1 \(\left(1, \frac{2}{3}\right)\)
2 \((3,1)\)
3 \((3,3)\)
4 \((1,2)\)
Explanation:
(C) :Given, differential equation. \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) Cubic on both sides, \(\left(1+3 \frac{d y}{d x}\right)^{2}=64\left(\frac{d^{3} y}{d x^{3}}\right)^{3}\) Hence, order and degree of the differential equation are 3 and 3 respectively.
CG PET-2018]**# / SRM JEEE-2016
Differential Equation
87098
The second order derivative of \(\frac{e^{x}+1}{e^{x}}\) is
1 \(e^{x}\)
2 \(\frac{1}{\mathrm{e}^{\mathrm{x}}}\)
3 \(\frac{e^{x}-1}{e^{x}}\)
4 \(e^{x}+\frac{1}{e^{x}}\)
Explanation:
(B) : Given \(y=\frac{e^{x}+1}{e^{x}}\) \(y=\frac{e^{x}}{e^{x}}+\frac{1}{e^{x}}\) \(\mathrm{y}=1+\frac{1}{\mathrm{e}^{\mathrm{x}}}\) Differentiating w.r.t. \(x\), we get - \(\frac{\mathrm{dy}}{\mathrm{dx}}=0+\left(-\mathrm{e}^{-\mathrm{x}}\right)\) Again differentiating w.r.t. \(x\), we get - \(\frac{d^{2} y}{d x^{2}}=-1(-1) e^{-x}=e^{-x}\) \(\frac{d^{2} y}{d x^{2}}=\frac{1}{e^{x}}\)
MHT CET-2004
Differential Equation
87099
The product of the degree and order of the D.E. \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) is
1 4
2 6
3 2
4 3
Explanation:
(A) : Given differential equation is \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) So, order \(=2\) and degree \(=2\) \(\therefore\) Product of the degree and order is, \(=2 \times 2=4\)
COMEDK-2015
Differential Equation
87101
The order and degree of the differential equation whose solution is \(\mathbf{y}=\mathbf{c x}+\mathbf{c}^{2}-3 \mathbf{c}^{3 / 2}+2\), where \(\mathbf{c}\) is a parameter, is
1 order \(=4\), degree \(=4\)
2 order \(=4\), degree \(=1\)
3 order \(=1\), degree \(=4\)
4 None of these
Explanation:
(C) : We have, \(y=c x+c^{2}-3 c^{3 / 2}+2 \tag{i}\) Differentiating both side with respect to \(\mathrm{x}\), we have \(\frac{d y}{d x}=c\) Putting this value of \(c\) in equation (i), we have \(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}-3\left(\frac{d y}{d x}\right)^{3 / 2}+2\) \(y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2=-3\left(\frac{d y}{d x}\right)^{3 / 2}\) Squaring both side, we have- \(\left[y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2\right]^{2}=9\left(\frac{d y}{d x}\right)^{3}\) So, order is 1 and degree is 4
87096
The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) are equal to
1 \(\left(1, \frac{2}{3}\right)\)
2 \((3,1)\)
3 \((3,3)\)
4 \((1,2)\)
Explanation:
(C) :Given, differential equation. \(\left(1+3 \frac{d y}{d x}\right)^{2 / 3}=4 \frac{d^{3} y}{d x^{3}}\) Cubic on both sides, \(\left(1+3 \frac{d y}{d x}\right)^{2}=64\left(\frac{d^{3} y}{d x^{3}}\right)^{3}\) Hence, order and degree of the differential equation are 3 and 3 respectively.
CG PET-2018]**# / SRM JEEE-2016
Differential Equation
87098
The second order derivative of \(\frac{e^{x}+1}{e^{x}}\) is
1 \(e^{x}\)
2 \(\frac{1}{\mathrm{e}^{\mathrm{x}}}\)
3 \(\frac{e^{x}-1}{e^{x}}\)
4 \(e^{x}+\frac{1}{e^{x}}\)
Explanation:
(B) : Given \(y=\frac{e^{x}+1}{e^{x}}\) \(y=\frac{e^{x}}{e^{x}}+\frac{1}{e^{x}}\) \(\mathrm{y}=1+\frac{1}{\mathrm{e}^{\mathrm{x}}}\) Differentiating w.r.t. \(x\), we get - \(\frac{\mathrm{dy}}{\mathrm{dx}}=0+\left(-\mathrm{e}^{-\mathrm{x}}\right)\) Again differentiating w.r.t. \(x\), we get - \(\frac{d^{2} y}{d x^{2}}=-1(-1) e^{-x}=e^{-x}\) \(\frac{d^{2} y}{d x^{2}}=\frac{1}{e^{x}}\)
MHT CET-2004
Differential Equation
87099
The product of the degree and order of the D.E. \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) is
1 4
2 6
3 2
4 3
Explanation:
(A) : Given differential equation is \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) So, order \(=2\) and degree \(=2\) \(\therefore\) Product of the degree and order is, \(=2 \times 2=4\)
COMEDK-2015
Differential Equation
87101
The order and degree of the differential equation whose solution is \(\mathbf{y}=\mathbf{c x}+\mathbf{c}^{2}-3 \mathbf{c}^{3 / 2}+2\), where \(\mathbf{c}\) is a parameter, is
1 order \(=4\), degree \(=4\)
2 order \(=4\), degree \(=1\)
3 order \(=1\), degree \(=4\)
4 None of these
Explanation:
(C) : We have, \(y=c x+c^{2}-3 c^{3 / 2}+2 \tag{i}\) Differentiating both side with respect to \(\mathrm{x}\), we have \(\frac{d y}{d x}=c\) Putting this value of \(c\) in equation (i), we have \(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}-3\left(\frac{d y}{d x}\right)^{3 / 2}+2\) \(y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2=-3\left(\frac{d y}{d x}\right)^{3 / 2}\) Squaring both side, we have- \(\left[y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^{2}-2\right]^{2}=9\left(\frac{d y}{d x}\right)^{3}\) So, order is 1 and degree is 4