What is the solution for y^{''}-81y=e^{10}t ?

The solution for y^{''}-81y=e^{10}t is y=c_{1}e^{9t}+c_{2}e^{-9t}-(e^{10}t)/(81)

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y^{''}-81y=e^{10}t

y^{^{''}} - 81 y = e^{10} t

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} - \frac{e ^{10} t}{81}

Solution steps

y^{''} (t) - 81 y = e^{10} t

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} - \frac{e ^{10} t}{81}

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} - \frac{e ^{10} t}{81}

y^{^{''}} - 7 y^{^{'}} + 6 y = sin (x)

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

y^{^{''}} + 7 y^{^{'}} + 6 y = 8

y^{^{''}} + 4 y = 3 sin (t), y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} - 4 y = 3 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}-81y=e^{10}t ?
The solution for y^{''}-81y=e^{10}t is y=c_{1}e^{9t}+c_{2}e^{-9t}-(e^{10}t)/(81)