What is the solution for y^{''}-81y=9,y(0)=1,y^'(0)=0 ?

The solution for y^{''}-81y=9,y(0)=1,y^'(0)=0 is y=(-5/9+10/9)e^{9t}+5/9 e^{-9t}-1/9

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y^{''}-81y=9,y(0)=1,y^'(0)=0

y^{^{''}} - 81 y = 9, y (0) = 1, y^{^{'}} (0) = 0

y = (- \frac{5}{9} + \frac{10}{9}) e^{9 t} + \frac{5}{9} e^{- 9 t} - \frac{1}{9}

Solution steps

y^{''} (t) - 81 y = 9

Solve linear ODE:

y = (- \frac{5}{9} + \frac{10}{9}) e^{9 t} + \frac{5}{9} e^{- 9 t} - \frac{1}{9}

y = (- \frac{5}{9} + \frac{10}{9}) e^{9 t} + \frac{5}{9} e^{- 9 t} - \frac{1}{9}

What is the solution for y^{''}-81y=9,y(0)=1,y^'(0)=0 ?
The solution for y^{''}-81y=9,y(0)=1,y^'(0)=0 is y=(-5/9+10/9)e^{9t}+5/9 e^{-9t}-1/9