What is the solution for y^{''}-9y^'=81t ?

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

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y^{''}-9y^'=81t

y^{^{''}} - 9 y^{^{'}} = 81 t

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

Solution steps

y^{''} (t) - 9 y^{'} (t) = 81 t

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{arccos ( x )}{x})

\frac{d}{d x} (tan (x) + \frac{1}{x ^{2}})

\int 4 - x d x

x \to - \infty lim (x^{2} + 2)

\int_{1}^{2} 3 x^{2} d x

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