What is the solution for y^{''}-3y^'-4y=4x^2 ?

The solution for y^{''}-3y^'-4y=4x^2 is y=c_{1}e^{4x}+c_{2}e^{-x}-x^2+(3x)/2-13/8

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y^{''}-3y^'-4y=4x^2

y^{^{''}} - 3 y^{^{'}} - 4 y = 4 x^{2}

y = c_{1} e^{4 x} + c_{2} e^{- x} - x^{2} + \frac{3 x}{2} - \frac{13}{8}

Solution steps

y^{''} (x) - 3 y^{'} (x) - 4 y = 4 x^{2}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- x} - x^{2} + \frac{3 x}{2} - \frac{13}{8}

y = c_{1} e^{4 x} + c_{2} e^{- x} - x^{2} + \frac{3 x}{2} - \frac{13}{8}

What is the solution for y^{''}-3y^'-4y=4x^2 ?
The solution for y^{''}-3y^'-4y=4x^2 is y=c_{1}e^{4x}+c_{2}e^{-x}-x^2+(3x)/2-13/8