What is the solution for (d^2y)/(dx^2)-y=19.2e^{4x}+60e^x ?

The solution for (d^2y)/(dx^2)-y=19.2e^{4x}+60e^x is y=c_{1}e^x+c_{2}e^{-x}+32/25 e^{4x}+30xe^x

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(d^2y)/(dx^2)-y=19.2e^{4x}+60e^x

\frac{d ^{2} y}{d x ^{2}} - y = 19.2 e^{4 x} + 60 e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = 19.2 e^{4 x} + 60 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

y^{^{''}} + 12 y^{^{'}} + 100 y = 48 sin (10 x)

y^{^{''}} - 16 y = 7 t, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} + 2 y - x - 3 = 0, y (0) = 0

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

y^{^{''}} - y = sin (3 x)

What is the solution for (d^2y)/(dx^2)-y=19.2e^{4x}+60e^x ?
The solution for (d^2y)/(dx^2)-y=19.2e^{4x}+60e^x is y=c_{1}e^x+c_{2}e^{-x}+32/25 e^{4x}+30xe^x