What is the solution for y^{''}-16y=9.6e^{4x}+30e^x ?

The solution for y^{''}-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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y^{''}-16y=9.6e^{4x}+30e^x

y^{^{''}} - 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

y^{''} (x) - 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^{^{''}} - y = 3 e^{2 x}

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 t} (cos (t) + 2 sin (t))

y^{^{'''}} + 6 y = 7 y^{^{'}} + 4 e^{x}

y^{^{''}} + y - 12 = 0

x^{^{''}} - 3 x^{^{'}} + 2 x = 20 sin (2 t)

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