The solution of the differential equation dy dx + y x = x^2 is - Vidyadip

MCQ

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

✓
$4xy = {x^4} + c$
B
$xy = {x^4} + c$
C
$\frac{1}{4}xy = {x^4} + c$
D
$xy = 4{x^4} + c$

✓

Answer

Correct option: A.

$4xy = {x^4} + c$

a
(a) The given equation $\frac{{dy}}{{dx}} + \frac{y}{x} = {x^2}$is of the form

$\frac{{dy}}{{dx}} + Py = Q$. So, $I.F.$= ${e^{\int_{}^{} {\frac{1}{x}dx} }} = {e^{\log x}} = x$

Hence required solution $xy = \int_{}^{} {x.{x^2}dx + c} $

==> $xy = \frac{{{x^4}}}{4} + c$ ==> $4xy = {x^4} + c$.

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