Question

find the solution of differential equation xdy/dx=y+xtany/x​

Answer 1

Answer:

find the solution of differential equation xdy/dx=y+xtany/x​

by dividing with x, we get

dy/dx=(y/x)+tany/x

let V=y/x

y=Vx

dy/dx=V+xdV/dx

hence

V+xdV/dx=V+ tanV

dV/tanV=dx/x

on integrating both the side

$\int {cotV} \, dV=\int {1/x} \, dx$

ln(sinV)=lnx+lnC

sinV=cx

V=arcsin(cx)

$y=xsinx^{-1}(Cx)$

Step-by-step explanation: