What is the solution for y^{''}-4y=9e^t,y(0)=0,y^'(0)=0 ?

The solution for y^{''}-4y=9e^t,y(0)=0,y^'(0)=0 is y=(-3/4+3)e^{2t}+3/4 e^{-2t}-3e^t

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y^{''}-4y=9e^t,y(0)=0,y^'(0)=0

y^{^{''}} - 4 y = 9 e^{t}, y (0) = 0, y^{^{'}} (0) = 0

y = (- \frac{3}{4} + 3) e^{2 t} + \frac{3}{4} e^{- 2 t} - 3 e^{t}

Solution steps

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

Solve linear ODE:

y = (- \frac{3}{4} + 3) e^{2 t} + \frac{3}{4} e^{- 2 t} - 3 e^{t}

y = (- \frac{3}{4} + 3) e^{2 t} + \frac{3}{4} e^{- 2 t} - 3 e^{t}

x \to - 1 lim (5 - 2 x - x^{2})

\int (2^{x} - 3^{x})^{0} d x

\frac{d}{d x} (7 sec (x) - 2 x)

\frac{d y}{d t} = - 3 (1 - y) (1 - 2 y)

\frac{d}{d y} (\frac{100 y}{x + y}) = 0

What is the solution for y^{''}-4y=9e^t,y(0)=0,y^'(0)=0 ?
The solution for y^{''}-4y=9e^t,y(0)=0,y^'(0)=0 is y=(-3/4+3)e^{2t}+3/4 e^{-2t}-3e^t