I'm trying to solve a Differential Equation using Mathematica to check whether the result I get is equal to the result I got by solving the equation by hand.
However, Mathematica gives me an answer including ProductLog which doesn't make sense to me.
Here is my differential equation:
y'[x] == x^2 + y[x]^2)/(x*y[x] - x^2)
This is my input to Mathematica:
DSolve[y'[x] == (x^2 + y[x]^2)/(x*y[x] - x^2), y[x], x]
This is the answer I got:
{{y[x] -> -x - 2 x ProductLog[-(E^(-(1/2) - C[1]/2)/(2 Sqrt[x]))]}}
The answer I got by solving by hand is:
y = xLn|((x+y)^2)/(x)| + Cx
C is the constant of integration.
Use Mathematica to solve for y in the solution you found by hand. The result involves ProductLog and looks very much like the soluiton Mathematica gives for your differential equation.