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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.

cconsta1
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Cworm
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1 Answers1

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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.

Laurence Wigton
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