Miscellaneous Application of Differential Equation
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Differential Equation

87627 The general solution of the differential equation \(y y^{\prime}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right]\) where \(\phi\) is an arbitrary function, is

1 \(x \phi\left(\frac{y^{2}}{x^{2}}\right)=c y\)
2 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{c}\)
3 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cy}^{2}\)
4 \(\phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cx}^{2}\)
AP EAMCET-20.04.2019
Differential Equation

87628 If \(c\) is a parameter, then the differential equation of the family of curves \(x^{2}=c(y+c)^{2}\) is

1 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}-1=0\)
2 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}+1=0\)
3 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}+1=0\)
4 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}-1=0\)
AP EAMCET-20.04.2019
Differential Equation

87629 If \(f(\mathrm{x}), f^{\prime}(\mathrm{x}), f^{\prime \prime}(\mathrm{x})\), are positive functions and \(f(0)=1, f^{\prime}(0)=2\), then the solution of the differential equation \(\left|\begin{array}{ll}f(0) &f^{\prime}(\mathrm{x}) \\ f^{\prime}(\mathrm{x}) &f^{\prime \prime}(\mathrm{x})\end{array}\right|=0\) is

1 \(e^{2 x}\)
2 \(2 \sin x+1\)
3 \(\sin ^{2} x+2 x+1\)
4 \(\mathrm{e}^{4 \mathrm{x}}\)
AP EAMCET-20.04.2019
Differential Equation

87630 \(y=A e^{x}+B e^{-2 x}\) satisfies which of the following differential equations?

1 \(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+2 y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}-y=0\)
3 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=0\)
4 \(\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-2 y=0\)
AP EAMCET-04.07.2022
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Differential Equation

87627 The general solution of the differential equation \(y y^{\prime}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right]\) where \(\phi\) is an arbitrary function, is

1 \(x \phi\left(\frac{y^{2}}{x^{2}}\right)=c y\)
2 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{c}\)
3 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cy}^{2}\)
4 \(\phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cx}^{2}\)
AP EAMCET-20.04.2019
Differential Equation

87628 If \(c\) is a parameter, then the differential equation of the family of curves \(x^{2}=c(y+c)^{2}\) is

1 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}-1=0\)
2 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}+1=0\)
3 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}+1=0\)
4 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}-1=0\)
AP EAMCET-20.04.2019
Differential Equation

87629 If \(f(\mathrm{x}), f^{\prime}(\mathrm{x}), f^{\prime \prime}(\mathrm{x})\), are positive functions and \(f(0)=1, f^{\prime}(0)=2\), then the solution of the differential equation \(\left|\begin{array}{ll}f(0) &f^{\prime}(\mathrm{x}) \\ f^{\prime}(\mathrm{x}) &f^{\prime \prime}(\mathrm{x})\end{array}\right|=0\) is

1 \(e^{2 x}\)
2 \(2 \sin x+1\)
3 \(\sin ^{2} x+2 x+1\)
4 \(\mathrm{e}^{4 \mathrm{x}}\)
AP EAMCET-20.04.2019
Differential Equation

87630 \(y=A e^{x}+B e^{-2 x}\) satisfies which of the following differential equations?

1 \(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+2 y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}-y=0\)
3 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=0\)
4 \(\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-2 y=0\)
AP EAMCET-04.07.2022
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Differential Equation

87627 The general solution of the differential equation \(y y^{\prime}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right]\) where \(\phi\) is an arbitrary function, is

1 \(x \phi\left(\frac{y^{2}}{x^{2}}\right)=c y\)
2 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{c}\)
3 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cy}^{2}\)
4 \(\phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cx}^{2}\)
AP EAMCET-20.04.2019
Differential Equation

87628 If \(c\) is a parameter, then the differential equation of the family of curves \(x^{2}=c(y+c)^{2}\) is

1 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}-1=0\)
2 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}+1=0\)
3 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}+1=0\)
4 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}-1=0\)
AP EAMCET-20.04.2019
Differential Equation

87629 If \(f(\mathrm{x}), f^{\prime}(\mathrm{x}), f^{\prime \prime}(\mathrm{x})\), are positive functions and \(f(0)=1, f^{\prime}(0)=2\), then the solution of the differential equation \(\left|\begin{array}{ll}f(0) &f^{\prime}(\mathrm{x}) \\ f^{\prime}(\mathrm{x}) &f^{\prime \prime}(\mathrm{x})\end{array}\right|=0\) is

1 \(e^{2 x}\)
2 \(2 \sin x+1\)
3 \(\sin ^{2} x+2 x+1\)
4 \(\mathrm{e}^{4 \mathrm{x}}\)
AP EAMCET-20.04.2019
Differential Equation

87630 \(y=A e^{x}+B e^{-2 x}\) satisfies which of the following differential equations?

1 \(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+2 y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}-y=0\)
3 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=0\)
4 \(\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-2 y=0\)
AP EAMCET-04.07.2022
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Differential Equation

87627 The general solution of the differential equation \(y y^{\prime}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right]\) where \(\phi\) is an arbitrary function, is

1 \(x \phi\left(\frac{y^{2}}{x^{2}}\right)=c y\)
2 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{c}\)
3 \(\mathrm{x}^{2} \phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cy}^{2}\)
4 \(\phi\left(\frac{\mathrm{y}^{2}}{\mathrm{x}^{2}}\right)=\mathrm{cx}^{2}\)
AP EAMCET-20.04.2019
Differential Equation

87628 If \(c\) is a parameter, then the differential equation of the family of curves \(x^{2}=c(y+c)^{2}\) is

1 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}-1=0\)
2 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}+1=0\)
3 \(x\left(\frac{d y}{d x}\right)^{3}+y\left(\frac{d y}{d x}\right)^{2}+1=0\)
4 \(x\left(\frac{d y}{d x}\right)^{3}-y\left(\frac{d y}{d x}\right)^{2}-1=0\)
AP EAMCET-20.04.2019
Differential Equation

87629 If \(f(\mathrm{x}), f^{\prime}(\mathrm{x}), f^{\prime \prime}(\mathrm{x})\), are positive functions and \(f(0)=1, f^{\prime}(0)=2\), then the solution of the differential equation \(\left|\begin{array}{ll}f(0) &f^{\prime}(\mathrm{x}) \\ f^{\prime}(\mathrm{x}) &f^{\prime \prime}(\mathrm{x})\end{array}\right|=0\) is

1 \(e^{2 x}\)
2 \(2 \sin x+1\)
3 \(\sin ^{2} x+2 x+1\)
4 \(\mathrm{e}^{4 \mathrm{x}}\)
AP EAMCET-20.04.2019
Differential Equation

87630 \(y=A e^{x}+B e^{-2 x}\) satisfies which of the following differential equations?

1 \(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+2 y=0\)
2 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}-y=0\)
3 \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=0\)
4 \(\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-2 y=0\)
AP EAMCET-04.07.2022