What is the solution for y^{''}-4y=9e^t ?

The solution for y^{''}-4y=9e^t is y=c_{1}e^{2t}+c_{2}e^{-2t}-3e^t

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y^{''}-4y=9e^t

y^{^{''}} - 4 y = 9 e^{t}

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

Solution steps

y^{''} (t) - 4 y = 9 e^{t}

Solve linear ODE:

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

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

\int 4 sec (4 x) tan (4 x) sec^{4} (4 x) d x

e^{- 4 x^{2}}

\frac{2}{( 1 + x ) ^{2}}

\int x e^{i x} d x

f (x) = 4 x^{3} - 24 x^{2}, at x = - 3

What is the solution for y^{''}-4y=9e^t ?
The solution for y^{''}-4y=9e^t is y=c_{1}e^{2t}+c_{2}e^{-2t}-3e^t