What is the solution for y^{''}-3y^'=18t ?

The solution for y^{''}-3y^'=18t is y=c_{1}e^{3t}+c_{2}-3t^2-2t

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y^{''}-3y^'=18t

y^{^{''}} - 3 y^{^{'}} = 18 t

y = c_{1} e^{3 t} + c_{2} - 3 t^{2} - 2 t

Solution steps

y^{''} (t) - 3 y^{'} (t) = 18 t

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} - 3 t^{2} - 2 t

y = c_{1} e^{3 t} + c_{2} - 3 t^{2} - 2 t

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What is the solution for y^{''}-3y^'=18t ?
The solution for y^{''}-3y^'=18t is y=c_{1}e^{3t}+c_{2}-3t^2-2t