What is the solution for y^{''}+6y^'+9y=3t+5 ?

The solution for y^{''}+6y^'+9y=3t+5 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+t/3+1/3

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y^{''}+6y^'+9y=3t+5

y^{^{''}} + 6 y^{^{'}} + 9 y = 3 t + 5

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 3 t + 5

Solve linear ODE:

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

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

\int (4 x^{3} - 3 x^{2} + 5) d x

\frac{d y}{d x} = \frac{x + y ^{2}}{2 y}

y = 2 x^{3} - 8 x

\int \frac{e ^{z} + 1}{e ^{z} + z} d z

\int (2 x + 4)^{2} + 2 x + 2 d x

What is the solution for y^{''}+6y^'+9y=3t+5 ?
The solution for y^{''}+6y^'+9y=3t+5 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+t/3+1/3