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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'}} - \frac{4}{x} y = \frac{( y ^{4} )}{x ^{9}}

\int 3 x^{2} + 3 d x

\frac{d}{d x} (x x + 4)

\frac{d y}{d x} = \frac{x}{7 y}

20 x - 50, 2 x^{2}, x = 0

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