What is the solution for y^{''}-4y=4e^{2x} ?

The solution for y^{''}-4y=4e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+e^{2x}x

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y^{''}-4y=4e^{2x}

y^{^{''}} - 4 y = 4 e^{2 x}

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

Solution steps

y^{''} (x) - 4 y = 4 e^{2 x}

Solve linear ODE:

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

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

\int e^{- \frac{x}{1000}} d x

\frac{d}{d x} (e^{3 l n (x)})

\int_{3}^{1} (- 5 x + 9) d x

\int \frac{1}{( x ^{2} + 5 ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (cos (n x) e^{n y})

What is the solution for y^{''}-4y=4e^{2x} ?
The solution for y^{''}-4y=4e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+e^{2x}x