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solve the differial equation
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xdy - ydx = [ ] x^2 + y^2 dxxdy/dx = y +  x^2 + y^2 dxdy/dx = y/x + 1 + { y/x } ^2put y = vx y = v + xdv/dx v + xdv/dx = v + 1 + v^21/ 1+ v^2 dv = (1/x) dx on itegratin log(v + 1 + v^2 ) = log x + C log ( (y/x) + 1 + (y/x)^2 ) = logx + logA where A > 0y/x + (x^2 + y^2 ) /x =Ax y/x + (x^2 + y^2 ) = Ax^2. |
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