Integrating factor of the equation ( x 2 + 1 ) d y d x + 2 x y = x 2 - 1 is:

Question

Integrating factor of the equation $(x^{2} + 1) \frac{d y}{d x} + 2 x y = x^{2} - 1$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $x^{2} + 1$

Explanation:

$\Rightarrow$ $\frac{d y}{d x} + \frac{2 x}{1 + x^{2}} y = \frac{x^{2} - 1}{x^{2} + 1}$

$I . F . = e^{\int \frac{2 x}{1 + x^{2}} d x}$

$= e^{\log (1 + x^{2})}$

$= 1 + x^{2}$

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