The particular solution of the differential equation $x d y+2 y d x=0$, when $x=2$ and $y=1$ is
The particular solution of the differential equation $x d y+2 y d x=0$, when $x=2$
and $y=1$ is
$x y^{2}=4$
$x^{2} y=4$
$x^{2} y=-4$
$x y^{2}=-4$
Solution
Given D.E. is $x d y+2 y d x=0$
$\therefore x d y=-2 y d x \Rightarrow \int \frac{d y}{y}=\int-\frac{2 d x}{x}$
$\log y=-2 \log x+\log c \Rightarrow \log y+2 \log x=\log c$
$\therefore \quad \log y+\log x^{2}=\log c \Rightarrow x^{2} y=c$
when $x=2, y=1, c=4$
$\therefore$ Particular solution is $\mathrm{x}^{2} \mathrm{y}=4$