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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The general solution of the differential equation $\frac{d y}{d x}=\frac{x^2}{y^2}$ is
  • ✓
    $x^3-y^3=c$
  • B
    $x^3+y^3=c$
  • C
    $x^2+y^2=c$
  • D
    $x^2-y^2=c$
✓

Answer

Correct option: A.
$x^3-y^3=c$
$\frac{d y}{d x}=\frac{x^2}{y^2}$
$\Rightarrow y^2 d y=x^2 d x$
$\Rightarrow \int y^2 d y=\int x^2 d x$
$\Rightarrow \frac{y^3}{3}=\frac{x^3}{3}+C$
$\Rightarrow x^3-y^3=-3 C=c \text { (say). }$

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