The solution of the differential equation, (x + 2y^3) dy dx = y i… - Vidyadip

MCQ

The solution of the differential equation, $(x + 2y^3) \frac{{dy}}{{dx}} = y$ is :

A
$\frac{x}{{{y^2}}} = y + c$
✓
$\frac{x}{{{y}}} = y^2 + c$
C
$\frac{{{x^2}}}{y} = y^2 + c$
D
$\frac{y}{x} = x^2 + c$

✓

Answer

Correct option: B.

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

b
$\frac{{dx}}{{dy}}\, = \,\frac{{x + 2{y^3}}}{y}$
$\frac{{dx}}{{dy}}\, - \,\frac{1}{y}\,x \,= 2y^2$ which is linear
$I.F. \, {e^{\int { - \frac{1}{y}dy} }} = e^{- ln y} = \frac{1}{y}$.
$\frac{1}{y} x = \int {\frac{1}{y}.2{y^2}\,dy} = y^2 + c $
$\frac{x}{y} = y^2 + c$

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