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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
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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