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

The solution for y^{''}-6y^'+9y=t is y=c_{1}e^{3t}+c_{2}te^{3t}+t/9+2/27

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

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

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{t}{9} + \frac{2}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{t}{9} + \frac{2}{27}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{t}{9} + \frac{2}{27}

\frac{d ^{2} y}{d x ^{2}} + 4 y = e^{4 x} sin (3 x)

y^{^{''}} - y = sinh (2 x)

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5 x}

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = e^{- t} sin (t)

y^{^{''}} + y^{^{'}} - 30 y = 2 x

What is the solution for y^{''}-6y^'+9y=t ?
The solution for y^{''}-6y^'+9y=t is y=c_{1}e^{3t}+c_{2}te^{3t}+t/9+2/27