What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=4x^2 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=4x^2 is y=c_{1}e^{2x}+c_{2}e^{-x}-2x^2+2x-3

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(d^2y)/(dx^2)-(dy)/(dx)-2y=4x^2

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

y = c_{1} e^{2 x} + c_{2} e^{- x} - 2 x^{2} + 2 x - 3

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - 2 x^{2} + 2 x - 3

y = c_{1} e^{2 x} + c_{2} e^{- x} - 2 x^{2} + 2 x - 3

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