What is the solution for y^{''}-3y^'-10y=54e^{7t} ?

The solution for y^{''}-3y^'-10y=54e^{7t} is y=c_{1}e^{5t}+c_{2}e^{-2t}+3e^{7t}

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y^{''}-3y^'-10y=54e^{7t}

y^{^{''}} - 3 y^{^{'}} - 10 y = 54 e^{7 t}

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 10 y = 54 e^{7 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = cos (4 x)

2 y^{^{'''}} - 5 y^{^{'}} + 3 y = 3 x^{2} e^{2 x}

y^{^{''}} - 6 y^{^{'}} + 8 y = - 2 e^{3 x}

y^{^{''}} + 5 y^{^{'}} - 5 y = 5 t + 9

y^{^{''}} + y = 3 x cos (x)

What is the solution for y^{''}-3y^'-10y=54e^{7t} ?
The solution for y^{''}-3y^'-10y=54e^{7t} is y=c_{1}e^{5t}+c_{2}e^{-2t}+3e^{7t}