Question

x*dy/dx=y-x*tan(y/x)

Answer 1

The given differential equation is,dydx = yx + tan-1yx .....1put y = vx⇒dydx = v + xdvdxNow, from 1, we getv + xdvdx = vxx + tan-1vxx⇒v + xdvdx = v + tan-1v⇒xdvdx = tan-1v⇒dvtan-1v = dxxIntegrating both sides,∫dvtan-1v = ∫ dxx ......2⇒∫dvtan-1v = logx + CThe integral obtained on the LHS of equation 2 can not be solved.Kindly recheck your question so that we wcould clear your doubt.



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