What is the solution for y^{''}-2y+y=12e^{3t} ?

The solution for y^{''}-2y+y=12e^{3t} is y=c_{1}e^t+c_{2}e^{-t}+3/2 e^{3t}

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y^{''}-2y+y=12e^{3t}

y^{^{''}} - 2 y + y = 12 e^{3 t}

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

Solution steps

y^{''} (t) - 2 y + y = 12 e^{3 t}

Solve linear ODE:

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

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

n = 0 \sum \infty \frac{1}{2 n + 2}

(2 + x) y^{^{'}} = 9 y

f (x) = 3 x + 55, at x = 3

x \to + 2 lim (\frac{g ( x )}{h ( x )})

\int tan^{2} (x) sec^{2} (x) sin (x) d x

What is the solution for y^{''}-2y+y=12e^{3t} ?
The solution for y^{''}-2y+y=12e^{3t} is y=c_{1}e^t+c_{2}e^{-t}+3/2 e^{3t}