What is the solution for y^{''}-9y=1,y(0)=0 ?

The solution for y^{''}-9y=1,y(0)=0 is y=(-c_{2}+1/9)e^{3t}+c_{2}e^{-3t}-1/9

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y^{''}-9y=1,y(0)=0

y^{^{''}} - 9 y = 1, y (0) = 0

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

Solution steps

y^{''} (t) - 9 y = 1

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = - 7 x + 4 x^{2}, y (0) = 0, y^{^{'}} (0) = 1

3 y^{^{''}} + 3 y^{^{'}} - 6 y = 4 e^{- 2 x}

y^{^{''}} + y = cos (\frac{- t + π}{2})

y^{^{''}} - y^{^{'}} - 6 y = 2 sin (3 x)

(D^{2} + 9) y = 4 cos (3 x)

What is the solution for y^{''}-9y=1,y(0)=0 ?
The solution for y^{''}-9y=1,y(0)=0 is y=(-c_{2}+1/9)e^{3t}+c_{2}e^{-3t}-1/9