Class 12

Math

Calculus

Differential Equations

Solve the differential equation $ye_{yx}dx=(xe_{yx}+y_{2})dy(y=0)$

$dydx =yx +e_{yx}y $

$ye_{yx}dydx =xe_{yx}+y_{2}$

$e_{yx}(y.dydx −x)=y_{2}$

let $yx =t$

$y_{2}dydx ⋅y−x =dt$

$e_{t}⋅(dydt )=1$

$∫e_{t}dt=∫dt$

$e_{t}=y+c$

$e_{yx}=y+c$

answer