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

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

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