Miscellaneous Application of Differential Equation
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Differential Equation

87642 The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

1 \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
4 \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
WB JEE-2020
Differential Equation

87643 If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

1 \(\mathrm{ce}^{\frac{\mathrm{x}^{2}}{2}}\)
2 \(\mathrm{ce}^{\mathrm{x}^{2}}\)
3 \(\mathrm{ce}^{2 \mathrm{x}^{2}}\)
4 \(\mathrm{ce}^{\mathrm{x}^{2 / 3}}\)
WB JEE-2022
Differential Equation

87644 The differential equation of all the ellipses centered at the origin and have axes as the coordinate axis is

1 \(y^{2}+x y^{2}-y y^{\prime}=0\)
2 \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
3 \(y y^{\prime \prime}+x y^{2}-x y^{\prime}=0\)
4 \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime}=\frac{d y}{d x}, y^{\prime \prime} \frac{d^{2} y}{d x^{2}}\)
WB JEE-2021
Differential Equation

87646 The population \(P=P(t)\) at time \(t\) of a certain species follows the differential equation \(\frac{d p}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

1 \(\log _{\mathrm{e}} 9\)
2 \(\frac{1}{2} \log _{\mathrm{e}} 18\)
3 \(\log _{\mathrm{e}} 18\)
4 \(2 \log _{\mathrm{e}} 18\)
JEE Main 24.02. Feb
Differential Equation

87647 Differential equations of the family of curves \(y\) \(=a \cos \mu x+b \sin \mu x\), where \(a\) and \(b\) are arbitrary constants is given by

1 \(\frac{d^{2} y}{d^{2}}+\mu y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-\mu^{2} y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+\mu^{2} y=0\)
4 None of these
Manipal UGET-2018]**#
NEET DIGITAL LIBRARY
Differential Equation

87642 The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

1 \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
4 \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
WB JEE-2020
Differential Equation

87643 If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

1 \(\mathrm{ce}^{\frac{\mathrm{x}^{2}}{2}}\)
2 \(\mathrm{ce}^{\mathrm{x}^{2}}\)
3 \(\mathrm{ce}^{2 \mathrm{x}^{2}}\)
4 \(\mathrm{ce}^{\mathrm{x}^{2 / 3}}\)
WB JEE-2022
Differential Equation

87644 The differential equation of all the ellipses centered at the origin and have axes as the coordinate axis is

1 \(y^{2}+x y^{2}-y y^{\prime}=0\)
2 \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
3 \(y y^{\prime \prime}+x y^{2}-x y^{\prime}=0\)
4 \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime}=\frac{d y}{d x}, y^{\prime \prime} \frac{d^{2} y}{d x^{2}}\)
WB JEE-2021
Differential Equation

87646 The population \(P=P(t)\) at time \(t\) of a certain species follows the differential equation \(\frac{d p}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

1 \(\log _{\mathrm{e}} 9\)
2 \(\frac{1}{2} \log _{\mathrm{e}} 18\)
3 \(\log _{\mathrm{e}} 18\)
4 \(2 \log _{\mathrm{e}} 18\)
JEE Main 24.02. Feb
Differential Equation

87647 Differential equations of the family of curves \(y\) \(=a \cos \mu x+b \sin \mu x\), where \(a\) and \(b\) are arbitrary constants is given by

1 \(\frac{d^{2} y}{d^{2}}+\mu y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-\mu^{2} y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+\mu^{2} y=0\)
4 None of these
Manipal UGET-2018]**#
Join With Us for More Updates
Differential Equation

87642 The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

1 \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
4 \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
WB JEE-2020
Differential Equation

87643 If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

1 \(\mathrm{ce}^{\frac{\mathrm{x}^{2}}{2}}\)
2 \(\mathrm{ce}^{\mathrm{x}^{2}}\)
3 \(\mathrm{ce}^{2 \mathrm{x}^{2}}\)
4 \(\mathrm{ce}^{\mathrm{x}^{2 / 3}}\)
WB JEE-2022
Differential Equation

87644 The differential equation of all the ellipses centered at the origin and have axes as the coordinate axis is

1 \(y^{2}+x y^{2}-y y^{\prime}=0\)
2 \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
3 \(y y^{\prime \prime}+x y^{2}-x y^{\prime}=0\)
4 \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime}=\frac{d y}{d x}, y^{\prime \prime} \frac{d^{2} y}{d x^{2}}\)
WB JEE-2021
Differential Equation

87646 The population \(P=P(t)\) at time \(t\) of a certain species follows the differential equation \(\frac{d p}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

1 \(\log _{\mathrm{e}} 9\)
2 \(\frac{1}{2} \log _{\mathrm{e}} 18\)
3 \(\log _{\mathrm{e}} 18\)
4 \(2 \log _{\mathrm{e}} 18\)
JEE Main 24.02. Feb
Differential Equation

87647 Differential equations of the family of curves \(y\) \(=a \cos \mu x+b \sin \mu x\), where \(a\) and \(b\) are arbitrary constants is given by

1 \(\frac{d^{2} y}{d^{2}}+\mu y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-\mu^{2} y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+\mu^{2} y=0\)
4 None of these
Manipal UGET-2018]**#
For More Updates join with Us
Differential Equation

87642 The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

1 \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
4 \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
WB JEE-2020
Differential Equation

87643 If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

1 \(\mathrm{ce}^{\frac{\mathrm{x}^{2}}{2}}\)
2 \(\mathrm{ce}^{\mathrm{x}^{2}}\)
3 \(\mathrm{ce}^{2 \mathrm{x}^{2}}\)
4 \(\mathrm{ce}^{\mathrm{x}^{2 / 3}}\)
WB JEE-2022
Differential Equation

87644 The differential equation of all the ellipses centered at the origin and have axes as the coordinate axis is

1 \(y^{2}+x y^{2}-y y^{\prime}=0\)
2 \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
3 \(y y^{\prime \prime}+x y^{2}-x y^{\prime}=0\)
4 \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime}=\frac{d y}{d x}, y^{\prime \prime} \frac{d^{2} y}{d x^{2}}\)
WB JEE-2021
Differential Equation

87646 The population \(P=P(t)\) at time \(t\) of a certain species follows the differential equation \(\frac{d p}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

1 \(\log _{\mathrm{e}} 9\)
2 \(\frac{1}{2} \log _{\mathrm{e}} 18\)
3 \(\log _{\mathrm{e}} 18\)
4 \(2 \log _{\mathrm{e}} 18\)
JEE Main 24.02. Feb
Differential Equation

87647 Differential equations of the family of curves \(y\) \(=a \cos \mu x+b \sin \mu x\), where \(a\) and \(b\) are arbitrary constants is given by

1 \(\frac{d^{2} y}{d^{2}}+\mu y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-\mu^{2} y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+\mu^{2} y=0\)
4 None of these
Manipal UGET-2018]**#
NEET DIGITAL LIBRARY
Differential Equation

87642 The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is

1 \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
4 \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
WB JEE-2020
Differential Equation

87643 If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

1 \(\mathrm{ce}^{\frac{\mathrm{x}^{2}}{2}}\)
2 \(\mathrm{ce}^{\mathrm{x}^{2}}\)
3 \(\mathrm{ce}^{2 \mathrm{x}^{2}}\)
4 \(\mathrm{ce}^{\mathrm{x}^{2 / 3}}\)
WB JEE-2022
Differential Equation

87644 The differential equation of all the ellipses centered at the origin and have axes as the coordinate axis is

1 \(y^{2}+x y^{2}-y y^{\prime}=0\)
2 \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
3 \(y y^{\prime \prime}+x y^{2}-x y^{\prime}=0\)
4 \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime}=\frac{d y}{d x}, y^{\prime \prime} \frac{d^{2} y}{d x^{2}}\)
WB JEE-2021
Differential Equation

87646 The population \(P=P(t)\) at time \(t\) of a certain species follows the differential equation \(\frac{d p}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

1 \(\log _{\mathrm{e}} 9\)
2 \(\frac{1}{2} \log _{\mathrm{e}} 18\)
3 \(\log _{\mathrm{e}} 18\)
4 \(2 \log _{\mathrm{e}} 18\)
JEE Main 24.02. Feb
Differential Equation

87647 Differential equations of the family of curves \(y\) \(=a \cos \mu x+b \sin \mu x\), where \(a\) and \(b\) are arbitrary constants is given by

1 \(\frac{d^{2} y}{d^{2}}+\mu y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-\mu^{2} y=0\)
3 \(\frac{d^{2} y}{d x^{2}}+\mu^{2} y=0\)
4 None of these
Manipal UGET-2018]**#