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in Differential equations by (36.3k points)

Solve: sin(x/y)(ydx – xdy) = xy3(xdy + ydx).

1 Answer

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Best answer

The given differential equation is 

sin(x/y) (ydx – xdy) = xy3(xdy + ydx)

sin(x/y) ((ydx – xdy)/y2) = xyd(xy)

sin(x/y) d(x/y) = xyd(xy)

Integrating, we get 

–cos(x/y) = ((xy)2/2) + c

which is the required solution.

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