What is the solution for y^{''}-36y=8,y(0)=1,y^'(0)=0 ?

The solution for y^{''}-36y=8,y(0)=1,y^'(0)=0 is y=(-11/18+11/9)e^{6t}+11/18 e^{-6t}-2/9

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y^{''}-36y=8,y(0)=1,y^'(0)=0

y^{^{''}} - 36 y = 8, y (0) = 1, y^{^{'}} (0) = 0

y = (- \frac{11}{18} + \frac{11}{9}) e^{6 t} + \frac{11}{18} e^{- 6 t} - \frac{2}{9}

Solution steps

y^{''} (t) - 36 y = 8

Solve linear ODE:

y = (- \frac{11}{18} + \frac{11}{9}) e^{6 t} + \frac{11}{18} e^{- 6 t} - \frac{2}{9}

y = (- \frac{11}{18} + \frac{11}{9}) e^{6 t} + \frac{11}{18} e^{- 6 t} - \frac{2}{9}

y^{^{'''}} - 36 y^{^{'}} = t e^{- 6 t} + 7 cos (6 t)

2 y^{^{''}} + 3 y^{^{'}} + y = g (t)

y^{^{''}} + y^{^{'}} = - 4 x + 2

y^{^{'''}} + 24 y^{^{''}} - 2048 y = e^{- 16 x}

(D^{2} - 1) y = (1 + e^{- x})^{- 2}

What is the solution for y^{''}-36y=8,y(0)=1,y^'(0)=0 ?
The solution for y^{''}-36y=8,y(0)=1,y^'(0)=0 is y=(-11/18+11/9)e^{6t}+11/18 e^{-6t}-2/9