What is the solution for y^{''}-4y=16xe^{2x} ?

The solution for y^{''}-4y=16xe^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+2x^2e^{2x}-e^{2x}x

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y^{''}-4y=16xe^{2x}

y^{^{''}} - 4 y = 16 x e^{2 x}

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

Solution steps

y^{''} (x) - 4 y = 16 x e^{2 x}

Solve linear ODE:

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

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

\frac{d y}{d t} + tan (t) y = 3 sin (t), y (0) = 1

\frac{d y}{d x} = \frac{3 x ^{2}}{y ( 1 - x ^{3} )}

\frac{d}{d x} (- 32 cos (8 x))

\frac{d}{d x} (\frac{2 x + 9}{2 x})

f (x) = x^{2} + x - 2

What is the solution for y^{''}-4y=16xe^{2x} ?
The solution for y^{''}-4y=16xe^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+2x^2e^{2x}-e^{2x}x