What is the solution for y^{''}-6y^'=9t ?

The solution for y^{''}-6y^'=9t is y=c_{1}e^{6t}+c_{2}-(3t^2)/4-t/4

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y^{''}-6y^'=9t

y^{^{''}} - 6 y^{^{'}} = 9 t

y = c_{1} e^{6 t} + c_{2} - \frac{3 t ^{2}}{4} - \frac{t}{4}

Solution steps

y^{''} (t) - 6 y^{'} (t) = 9 t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} - \frac{3 t ^{2}}{4} - \frac{t}{4}

y = c_{1} e^{6 t} + c_{2} - \frac{3 t ^{2}}{4} - \frac{t}{4}

f (x) = 19 x e^{x}

\int sin (x) e^{3 x} d x

\int x^{2} cos (\frac{1}{9} x) d x

\frac{d}{d x} (sec (x) tan^{2} (x))

\frac{\partial}{\partial x} (\frac{x ^{2} - y}{x ^{2} + y})

What is the solution for y^{''}-6y^'=9t ?
The solution for y^{''}-6y^'=9t is y=c_{1}e^{6t}+c_{2}-(3t^2)/4-t/4