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}}

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (9)

\frac{d y}{d x} = \frac{4 x ^{2}}{7 y}

\frac{d y}{d x} + 4 y = 20, y (0) = 2

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

y^{^{'}} = sin (2 x) y^{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)