Class 12

Math

Calculus

Differential Equations

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=a_{2}−x_{2} x∈(−x,a)$ : $x+ydxdy =0(y=0)$

Squaring both sides,

$⇒y_{2}=a_{2}−x_{2}$

Differentiating both sides w.r.t. $x$,

$⇒2ydxdy =0−2x$

$⇒ydxdy =−x$

$⇒x+ydxdy =0$

So, given function is a solution of the corresponding differential equation.