What is the solution for (d^2y)/(dx^2)-16y=9e^{4x}+30e^x ?

The solution for (d^2y)/(dx^2)-16y=9e^{4x}+30e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(9e^{4x}x)/8-2e^x

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(d^2y)/(dx^2)-16y=9e^{4x}+30e^x

\frac{d ^{2} y}{d x ^{2}} - 16 y = 9 e^{4 x} + 30 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{9 e ^{4 x} x}{8} - 2 e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 y = 9 e^{4 x} + 30 e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{9 e ^{4 x} x}{8} - 2 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{9 e ^{4 x} x}{8} - 2 e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y^{^{'}} = x^{2}

2 y^{^{''}} + 3 y^{^{'}} + y = lo g_{10} (x)

2 y^{^{''}} + 18 y = 6 tan (3 t)

x^{^{''}} - 5 x^{^{'}} - 6 x = 2 e^{- 3 t}

3 y^{^{''}} + 2 g^{2} y = 4.9 g cos (8 t)

What is the solution for (d^2y)/(dx^2)-16y=9e^{4x}+30e^x ?
The solution for (d^2y)/(dx^2)-16y=9e^{4x}+30e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(9e^{4x}x)/8-2e^x