What is the solution for y^{''}-6y^'+9y=2e^{3t} ?

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

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y^{''}-6y^'+9y=2e^{3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{3 t}

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 2 e^{3 t}

Solve linear ODE:

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

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

\int \frac{- 2 sec ^{2} ( x )}{( 4 + tan ( x ) ) ^{3}} d x

y = e^{9 e^{x}}

x (\frac{d y}{d x}) + y = \frac{1}{y ^{2}}

y = x x

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

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