Integrating factor of equation ( x^2 + 1) dy dx + 2xy = x^2 - 1 i… - Vidyadip

MCQ

Integrating factor of equation $({x^2} + 1)\frac{{dy}}{{dx}} + 2xy = {x^2} - 1$ is

✓
${x^2} + 1$
B
$\frac{{2x}}{{{x^2} + 1}}$
C
$\frac{{{x^2} - 1}}{{{x^2} + 1}}$
D
None of these

✓

Answer

Correct option: A.

${x^2} + 1$

a
(a) $\frac{{dy}}{{dx}} + \frac{{2x}}{{1 + {x^2}}}y = \frac{{{x^2} - 1}}{{{x^2} + 1}}$

$I.F.$ $ = {e^{\int {\frac{{2x}}{{1 + {x^2}}}dx} }} = {e^{\log (1 + {x^2})}}$$ = 1 + {x^2}$.

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