The general solution of the differential equation dydx-2xy1-x2-0 is

The correct option is A y=A(1+x^2) dydx=2xy1+x^2 dyy=2x1+x^2dx ⇒ log y=log C(1+x^2) y=C(1+x^2) ...

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Standard XII

Mathematics

Integrating Factor

The general s...

Question

The general solution of the differential equation $\frac{d y}{d x} - \frac{2 x y}{1 + x^{2}} = 0$ is

y = A (1 + x^{2})

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y = A \sqrt{1 + x^{2}}

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y = \frac{A}{1 + x^{2}}

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y = \frac{a}{\sqrt{1 + x^{2}}}

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Solution

The correct option is A $y = A (1 + x^{2})$
$\frac{d y}{d x} = \frac{2 x y}{1 + x^{2}}$
$\frac{d y}{y} = \frac{2 x}{1 + x^{2}} d x$
$\Rightarrow l o g y = l o g C (1 + x^{2})$
$y = C (1 + x^{2})$

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The general solution of the differential equation dydx−2xy1+x2=0 is

The correct option is A y=A(1+x2)dydx=2xy1+x2dyy=2x1+x2dx⇒logy=logC(1+x2)y=C(1+x2)

The general solution of the differential equation $\frac{d y}{d x} - \frac{2 x y}{1 + x^{2}} = 0$ is

The correct option is A $y = A (1 + x^{2})$
$\frac{d y}{d x} = \frac{2 x y}{1 + x^{2}}$
$\frac{d y}{y} = \frac{2 x}{1 + x^{2}} d x$
$\Rightarrow l o g y = l o g C (1 + x^{2})$
$y = C (1 + x^{2})$