What is the solution for (d^2y)/(dx^2)-4y=10e^{3x} ?

The solution for (d^2y)/(dx^2)-4y=10e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+2e^{3x}

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(d^2y)/(dx^2)-4y=10e^{3x}

\frac{d ^{2} y}{d x ^{2}} - 4 y = 10 e^{3 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 y = 10 e^{3 x}

Solve linear ODE:

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

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

x^{^{''}} + 2 x^{^{'}} + x = cos (2 t) + 3 sin (2 t)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = x^{3} + 6

y^{^{''}} + 8 y^{^{'}} + 17 y = 17 x^{2} - x + 28

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = e^{- 2 x}

y^{^{''}} - 4 y^{^{'}} + 5 y = 5 t

What is the solution for (d^2y)/(dx^2)-4y=10e^{3x} ?
The solution for (d^2y)/(dx^2)-4y=10e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+2e^{3x}