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Question

Solution of the differential equation
yex/ydx=(xex/y+y2siny)dy, is

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Solution

Given,

yexydx=(xexy+y2siny)dy

exydx=(xyexy+ysiny)dy

dxdy=xy+ysinyexy

substitute v=xydxdy=ydvdy+v

ydvdy+v=v+ysinyev

ydvdy=ysinyev

evdv=sinydy

integrating on both sides, ev=cosy+c

exy+cosy=c

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