What is the solution for y^{''}-8y^'-9y=21e^2t ?

The solution for y^{''}-8y^'-9y=21e^2t is y=c_{1}e^{9t}+c_{2}e^{-t}-(7e^2t)/3+(56e^2)/(27)

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y^{''}-8y^'-9y=21e^2t

y^{^{''}} - 8 y^{^{'}} - 9 y = 21 e^{2} t

y = c_{1} e^{9 t} + c_{2} e^{- t} - \frac{7 e ^{2} t}{3} + \frac{56 e ^{2}}{27}

Solution steps

y^{''} (t) - 8 y^{'} (t) - 9 y = 21 e^{2} t

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- t} - \frac{7 e ^{2} t}{3} + \frac{56 e ^{2}}{27}

y = c_{1} e^{9 t} + c_{2} e^{- t} - \frac{7 e ^{2} t}{3} + \frac{56 e ^{2}}{27}

y^{^{''}} + 4 y^{^{'}} = 3 \cdot sin (2 x)

y^{^{''}} - 6 y^{^{'}} + 8 y = x e^{3 x} cos (4 x)

y^{^{''}} - 8 y^{^{'}} - 20 y = 5 e^{- 2 x}

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{4} x

y^{^{''}} + 9 y^{^{'}} = sin (t), y (0) = 1, y^{^{'}} (0) = 1

What is the solution for y^{''}-8y^'-9y=21e^2t ?
The solution for y^{''}-8y^'-9y=21e^2t is y=c_{1}e^{9t}+c_{2}e^{-t}-(7e^2t)/3+(56e^2)/(27)