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

The solution for y^{''}+6y^'+9y=t+e^{3t} is y=c_{1}e^{-3t}+c_{2}te^{-3t}+t/9-2/27+1/36 e^{3t}

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

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

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27} + \frac{1}{36} e^{3 t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27} + \frac{1}{36} e^{3 t}

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27} + \frac{1}{36} e^{3 t}

\int \frac{x ^{2} + 5 x + 12}{x} d x

x y - 5 y^{2} = 4, (12, 2)

x \to 0 lim (\frac{2 sin ( x )}{x})

\frac{d}{d x} (\frac{x}{( x - 1 ) ^{\frac{2}{3}} ( x + 2 ) ^{\frac{1}{3}}})

\frac{d}{d x} (x^{2} y^{4} e^{y} - x^{2} y^{2} - 3 x)

What is the solution for y^{''}+6y^'+9y=t+e^{3t} ?
The solution for y^{''}+6y^'+9y=t+e^{3t} is y=c_{1}e^{-3t}+c_{2}te^{-3t}+t/9-2/27+1/36 e^{3t}