What is the solution for y^{''}-9y=2t^2+3t+9 ?

The solution for y^{''}-9y=2t^2+3t+9 is y=c_{1}e^{3t}+c_{2}e^{-3t}-(2t^2)/9-t/3-85/81

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y^{''}-9y=2t^2+3t+9

y^{^{''}} - 9 y = 2 t^{2} + 3 t + 9

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{2 t ^{2}}{9} - \frac{t}{3} - \frac{85}{81}

Solution steps

y^{''} (t) - 9 y = 2 t^{2} + 3 t + 9

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{2 t ^{2}}{9} - \frac{t}{3} - \frac{85}{81}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{2 t ^{2}}{9} - \frac{t}{3} - \frac{85}{81}

\frac{d}{d x} (3 x^{2} + e^{2 x} + π^{2})

n = 1 \sum \infty \frac{n}{6 n ^{2} - 5}

x \to + 4 - lim (\frac{2 x}{16 - x ^{2}})

y^{^{'}} = y^{2} (1 + x^{3})

\int (3 x + 2 e^{x})^{2} d x

What is the solution for y^{''}-9y=2t^2+3t+9 ?
The solution for y^{''}-9y=2t^2+3t+9 is y=c_{1}e^{3t}+c_{2}e^{-3t}-(2t^2)/9-t/3-85/81