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Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations2 Marks
Question
Solve the differential equation $y \frac{d y}{d x}+x=0$
✓

Answer

$y \frac{d y}{d x}+x=0$
$\therefore y \frac{d y}{d x}=-x$
$\therefore y d y=-x d x$
Integrating both sides,
$\int y d y=-\int x d x$
$\therefore \frac{y^2}{2}=-\frac{x^2}{2}+c_1$
$\therefore x^2+y^2=c$ where $c=2 c_1$
is the general solution.

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