Solution of differential equation x dy dx = y + x^ ^2 is - Vidyadip

MCQ

Solution of differential equation $x\frac{{dy}}{{dx}} = y + {x^{^2}}$ is

A
$y = {\log _e}x + \frac{{{x^2}}}{2} + a$
B
$y = \frac{{{x^3}}}{3} + \frac{a}{x}$
✓
$y = {x^2} + ax$
D
None of these

✓

Answer

Correct option: C.

$y = {x^2} + ax$

c
(c) $\frac{{dy}}{{dx}} - \frac{y}{x} = x$; $I.F.$ $ = {e^{\int_{}^{} { - \frac{1}{x}dx} }} = \frac{1}{x}$

$\therefore $ Solution is $y \cdot \frac{1}{x} = \int_{}^{} {x \cdot \frac{1}{x}dx} $

==> $\frac{y}{x} = x + a$ ==> $y = {x^2} + ax$.

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