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

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

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

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

y = \frac{x}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

y = \frac{x}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

\int 10 x^{2} ln (x) d x

\int \frac{y ^{2} + 18 y + 81}{( y ^{2} + 81 ) ^{2}} d y

(y + x y) d x - 2 x d y = 0

e^{2 x} + e^{- x}

\int \frac{1}{9 - x} d x

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