What is the solution for y^{''}-16y=19.2e^{4x}+60e^x ?

The solution for y^{''}-16y=19.2e^{4x}+60e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(12e^{4x}x)/5-4e^x

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y^{''}-16y=19.2e^{4x}+60e^x

y^{^{''}} - 16 y = 19.2 e^{4 x} + 60 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{12 e ^{4 x} x}{5} - 4 e^{x}

Solution steps

y^{''} (x) - 16 y = 19.2 e^{4 x} + 60 e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{12 e ^{4 x} x}{5} - 4 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{12 e ^{4 x} x}{5} - 4 e^{x}

What is the solution for y^{''}-16y=19.2e^{4x}+60e^x ?
The solution for y^{''}-16y=19.2e^{4x}+60e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(12e^{4x}x)/5-4e^x