Solve the following differential equations : x d x+2 y d y=0 - Vidyadip

Question

Solve the following differential equations : $x d x+2 y d y=0$

✓

Answer

$
x d x+2 y d y=0
$
Integrating, we get
$
\begin{aligned}
& \int xdx +2 \int ydy = c _1 \\
& \therefore \frac{x^2}{2}+2\left(\frac{y^2}{2}\right)=c_1 \\
& \therefore x ^2+2 y ^2=c_{\text {, }} \text { where } c =2 c _1
\end{aligned}
$
This is the general solution.

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