What is the solution for (d^2y)/(dx^2)-16y=9.6e^{4x}+30e^x ?

The solution for (d^2y)/(dx^2)-16y=9.6e^{4x}+30e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(6e^{4x}x)/5-2e^x

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(d^2y)/(dx^2)-16y=9.6e^{4x}+30e^x

\frac{d ^{2} y}{d x ^{2}} - 16 y = 9.6 e^{4 x} + 30 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{6 e ^{4 x} x}{5} - 2 e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 y = 9.6 e^{4 x} + 30 e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{6 e ^{4 x} x}{5} - 2 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{6 e ^{4 x} x}{5} - 2 e^{x}

y^{^{'''}} = 3 y^{^{''}} + 9 (e^{2 x}) + 5 (cos (x))

y^{^{''}} + 7 y^{^{'}} + 10 y = 7 u

y^{^{''}} + 4 y = cos (x), y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + y^{^{'}} = 3 x^{2} + 10 x

3 y^{^{''}} + 2 (9.81)^{2} y = 49 (9.81) cos (8 t)

What is the solution for (d^2y)/(dx^2)-16y=9.6e^{4x}+30e^x ?
The solution for (d^2y)/(dx^2)-16y=9.6e^{4x}+30e^x is y=c_{1}e^{4x}+c_{2}e^{-4x}+(6e^{4x}x)/5-2e^x