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Question Number 82245 by jagoll last updated on 19/Feb/20

find the solution x sin ((y/x)) dy = [y sin ((y/x)) −x] dx

findthesolutionxsin(yx)dy=[ysin(yx)−x]dx

Commented by john santu last updated on 19/Feb/20

let v = (y/x) ⇒ y = vx (dy/dx) = v + (dv/dx) ⇒ dy =v dx+ dv (x sin v)(v dx + dv) = [vx sin v−x]dx xv sin v dx + xsin v dv = xv sin v dx−x dx x sin v dv = −x dx sin v dv = −dx ⇒∫ sin v dv = −x+c −cos v = −x +c cos ((y/x)) = x + C

letv=yx⇒y=vxdydx=v+dvdx⇒dy=vdx+dv(xsinv)(vdx+dv)=[vxsinv−x]dxxvsinvdx+xsinvdv=xvsinvdx−xdxxsinvdv=−xdxsinvdv=−dx⇒∫sinvdv=−x+c−cosv=−x+ccos(yx)=x+C

Commented by jagoll last updated on 19/Feb/20

thank sir

thanksir

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