Homogeneous Differential Equation
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Differential Equation

87485 Let \(y=y(x)\) be the solution of the differential equation \(\left(x-x^{3}\right) d y=\left(y+y x^{2}-3 x^{4}\right) d x, x>2\). If \(y(3)=3\), then \(y(4)\) is equal to

1 4
2 12
3 8
4 16
Shift-II]**#
Differential Equation

87486 If \(y=\left(\frac{2 x}{\pi}-1\right) \operatorname{cosec} x\) is the solution of the differential equation, \(\frac{d y}{d x}+p(x) y=\frac{2}{\pi} \operatorname{cosec} x, 0\lt \) \(x\lt \frac{x}{2}\), then the function \(p(x)\) is equal to

1 \(\cot x\)
2 \(\cosec x\)
3 \(\sec x\)
4 \(\tan x\)
JEE Main 06.09.2020
Differential Equation

87487 If \(\frac{d y}{d x}+2 x \tan (x-y)=1\), then \(\sin (x-y)\) is equal

1 \(\mathrm{Ae}^{-\mathrm{x}^{2}}\)
2 \(\mathrm{Ae}^{2 \mathrm{x}}\)
3 \(\mathrm{Ae}^{\mathrm{x}^{2}}\)
4 \(\mathrm{Ae}^{-2 \mathrm{x}}\)
AP EAMCET-2012
Differential Equation

87488 The solution of the differential equation \(\sqrt{1-y^{2}} d x+x d y-\sin ^{-1} y d y=0\) is

1 \(x=\sin ^{-1} y-1+\operatorname{ce}^{-\sin ^{-1} y}\)
2 \(y=x \sqrt{1-y^{2}}+\sin ^{-1} y+c\)
3 \(x=1+\sin ^{-1} y+c e^{\sin -1} y\)
4 \(y=\sin ^{-1} y-1+x \sqrt{1-y^{2}+c}\)
TS EAMCET-03.05.2019
NEET DIGITAL LIBRARY
Differential Equation

87485 Let \(y=y(x)\) be the solution of the differential equation \(\left(x-x^{3}\right) d y=\left(y+y x^{2}-3 x^{4}\right) d x, x>2\). If \(y(3)=3\), then \(y(4)\) is equal to

1 4
2 12
3 8
4 16
Shift-II]**#
Differential Equation

87486 If \(y=\left(\frac{2 x}{\pi}-1\right) \operatorname{cosec} x\) is the solution of the differential equation, \(\frac{d y}{d x}+p(x) y=\frac{2}{\pi} \operatorname{cosec} x, 0\lt \) \(x\lt \frac{x}{2}\), then the function \(p(x)\) is equal to

1 \(\cot x\)
2 \(\cosec x\)
3 \(\sec x\)
4 \(\tan x\)
JEE Main 06.09.2020
Differential Equation

87487 If \(\frac{d y}{d x}+2 x \tan (x-y)=1\), then \(\sin (x-y)\) is equal

1 \(\mathrm{Ae}^{-\mathrm{x}^{2}}\)
2 \(\mathrm{Ae}^{2 \mathrm{x}}\)
3 \(\mathrm{Ae}^{\mathrm{x}^{2}}\)
4 \(\mathrm{Ae}^{-2 \mathrm{x}}\)
AP EAMCET-2012
Differential Equation

87488 The solution of the differential equation \(\sqrt{1-y^{2}} d x+x d y-\sin ^{-1} y d y=0\) is

1 \(x=\sin ^{-1} y-1+\operatorname{ce}^{-\sin ^{-1} y}\)
2 \(y=x \sqrt{1-y^{2}}+\sin ^{-1} y+c\)
3 \(x=1+\sin ^{-1} y+c e^{\sin -1} y\)
4 \(y=\sin ^{-1} y-1+x \sqrt{1-y^{2}+c}\)
TS EAMCET-03.05.2019
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Differential Equation

87485 Let \(y=y(x)\) be the solution of the differential equation \(\left(x-x^{3}\right) d y=\left(y+y x^{2}-3 x^{4}\right) d x, x>2\). If \(y(3)=3\), then \(y(4)\) is equal to

1 4
2 12
3 8
4 16
Shift-II]**#
Differential Equation

87486 If \(y=\left(\frac{2 x}{\pi}-1\right) \operatorname{cosec} x\) is the solution of the differential equation, \(\frac{d y}{d x}+p(x) y=\frac{2}{\pi} \operatorname{cosec} x, 0\lt \) \(x\lt \frac{x}{2}\), then the function \(p(x)\) is equal to

1 \(\cot x\)
2 \(\cosec x\)
3 \(\sec x\)
4 \(\tan x\)
JEE Main 06.09.2020
Differential Equation

87487 If \(\frac{d y}{d x}+2 x \tan (x-y)=1\), then \(\sin (x-y)\) is equal

1 \(\mathrm{Ae}^{-\mathrm{x}^{2}}\)
2 \(\mathrm{Ae}^{2 \mathrm{x}}\)
3 \(\mathrm{Ae}^{\mathrm{x}^{2}}\)
4 \(\mathrm{Ae}^{-2 \mathrm{x}}\)
AP EAMCET-2012
Differential Equation

87488 The solution of the differential equation \(\sqrt{1-y^{2}} d x+x d y-\sin ^{-1} y d y=0\) is

1 \(x=\sin ^{-1} y-1+\operatorname{ce}^{-\sin ^{-1} y}\)
2 \(y=x \sqrt{1-y^{2}}+\sin ^{-1} y+c\)
3 \(x=1+\sin ^{-1} y+c e^{\sin -1} y\)
4 \(y=\sin ^{-1} y-1+x \sqrt{1-y^{2}+c}\)
TS EAMCET-03.05.2019
For More Updates join with Us
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Differential Equation

87485 Let \(y=y(x)\) be the solution of the differential equation \(\left(x-x^{3}\right) d y=\left(y+y x^{2}-3 x^{4}\right) d x, x>2\). If \(y(3)=3\), then \(y(4)\) is equal to

1 4
2 12
3 8
4 16
Shift-II]**#
Differential Equation

87486 If \(y=\left(\frac{2 x}{\pi}-1\right) \operatorname{cosec} x\) is the solution of the differential equation, \(\frac{d y}{d x}+p(x) y=\frac{2}{\pi} \operatorname{cosec} x, 0\lt \) \(x\lt \frac{x}{2}\), then the function \(p(x)\) is equal to

1 \(\cot x\)
2 \(\cosec x\)
3 \(\sec x\)
4 \(\tan x\)
JEE Main 06.09.2020
Differential Equation

87487 If \(\frac{d y}{d x}+2 x \tan (x-y)=1\), then \(\sin (x-y)\) is equal

1 \(\mathrm{Ae}^{-\mathrm{x}^{2}}\)
2 \(\mathrm{Ae}^{2 \mathrm{x}}\)
3 \(\mathrm{Ae}^{\mathrm{x}^{2}}\)
4 \(\mathrm{Ae}^{-2 \mathrm{x}}\)
AP EAMCET-2012
Differential Equation

87488 The solution of the differential equation \(\sqrt{1-y^{2}} d x+x d y-\sin ^{-1} y d y=0\) is

1 \(x=\sin ^{-1} y-1+\operatorname{ce}^{-\sin ^{-1} y}\)
2 \(y=x \sqrt{1-y^{2}}+\sin ^{-1} y+c\)
3 \(x=1+\sin ^{-1} y+c e^{\sin -1} y\)
4 \(y=\sin ^{-1} y-1+x \sqrt{1-y^{2}+c}\)
TS EAMCET-03.05.2019
NEET DIGITAL LIBRARY