What is the solution for y^{''}-9y^'=81t,y(0)=9,y^'(0)=0 ?

The solution for y^{''}-9y^'=81t,y(0)=9,y^'(0)=0 is y=(9-80/9)e^{9t}+80/9-(9t^2)/2-t

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y^{''}-9y^'=81t,y(0)=9,y^'(0)=0

y^{^{''}} - 9 y^{^{'}} = 81 t, y (0) = 9, y^{^{'}} (0) = 0

y = (9 - \frac{80}{9}) e^{9 t} + \frac{80}{9} - \frac{9 t ^{2}}{2} - t

Solution steps

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

Solve linear ODE:

y = (9 - \frac{80}{9}) e^{9 t} + \frac{80}{9} - \frac{9 t ^{2}}{2} - t

y = (9 - \frac{80}{9}) e^{9 t} + \frac{80}{9} - \frac{9 t ^{2}}{2} - t

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What is the solution for y^{''}-9y^'=81t,y(0)=9,y^'(0)=0 ?
The solution for y^{''}-9y^'=81t,y(0)=9,y^'(0)=0 is y=(9-80/9)e^{9t}+80/9-(9t^2)/2-t