The general solution of the differential equation dy dx + 2 x y =… - Vidyadip

MCQ

The general solution of the differential equation $\frac{{dy}}{{dx}} + \frac{2}{x}y = {x^2}$ is

A
$y = c{x^{ - 3}} - \frac{{{x^2}}}{4}$
B
$y = c{x^3} - \frac{{{x^2}}}{4}$
C
$y = c{x^2} + \frac{{{x^3}}}{5}$
✓
$y = c{x^{-2}} + \frac{{{x^3}}}{5}$

✓

Answer

Correct option: D.

$y = c{x^{-2}} + \frac{{{x^3}}}{5}$

d
Given differential equation is

$\frac{d y}{d x}+\frac{2}{x}, y=x^{2}$

This is of thelinear form

$\therefore P=\frac{2}{x}, Q=x^{2}$

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

Solution is

$y \cdot x^{2}=\int x^{2} x^{2} d x+c=\frac{x^{5}}{5}+c$

$y=\frac{x^{3}}{5}+c x^{-2}$

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