What is the solution for y^'=e^{2x}+y*e^{2x} ?

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

(x - 1)^{2} y^{^{'}} + 8 (x - 1) y^{^{'}} + 12 y = 0

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

y^{^{'}} = \frac{2 y ^{4} + 2}{4 x y ^{3}}

y^{^{'}} = y + 5, y (0) = 11 e^{x} - 5

\frac{d y}{d x} = e^{(6 y + 7 x)}, y (0) = 15

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