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anonymous
 5 years ago
Show that the transformation, v =yx reduces the equation of the form yf(xy)dx + xg(xy)dy=0 to the form in which variables are separable in v and x,where f(xy)=g(xy) .Investigate the case f(xy)=g(xy)
anonymous
 5 years ago
Show that the transformation, v =yx reduces the equation of the form yf(xy)dx + xg(xy)dy=0 to the form in which variables are separable in v and x,where f(xy)=g(xy) .Investigate the case f(xy)=g(xy)

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Owlfred
 5 years ago
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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here if we assume y=f(xy)=g(xy), lets solve the problem backward, from yf(xy)dx + xg(xy)dy=0 becomes y ydx + xydy=0 if we let y=vx and dy=vdx+xdv, we get v^2x^2 dx + vx^2(vdx+xdv) =0 v^2dx + v^2dx +xvdv=0 2v^2dx+xvdv=0 dx/x + dv/2v=0 2dx/x + dv/v=0 2lnx + lnv=ln c lnx^2 + ln(y/x)=ln c lnxy=ln c xy=c
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