What is the solution for e^2xy^'+2e^2xy=2x ?

The solution for e^2xy^'+2e^2xy=2x is y=-e^{-2x-c_{1}-2}+1/(e^2)

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e^2xy^'+2e^2xy=2x

e^{2} x y^{^{'}} + 2 e^{2} x y = 2 x

y = - e^{- 2 x - c_{1} - 2} + \frac{1}{e ^{2}}

Solution steps

e^{2} x y^{'} (x) + 2 e^{2} x y = 2 x

Solve separable ODE:

y = - e^{- 2 x - c_{1} - 2} + \frac{1}{e ^{2}}

y = - e^{- 2 x - c_{1} - 2} + \frac{1}{e ^{2}}

What is the solution for e^2xy^'+2e^2xy=2x ?
The solution for e^2xy^'+2e^2xy=2x is y=-e^{-2x-c_{1}-2}+1/(e^2)