What is the solution for y^{''}-9y=0,y(0)=1,y^'(0)=15 ?

The solution for y^{''}-9y=0,y(0)=1,y^'(0)=15 is y=3e^{3t}-2e^{-3t}

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y^{''}-9y=0,y(0)=1,y^'(0)=15

y^{^{''}} - 9 y = 0, y (0) = 1, y^{^{'}} (0) = 15

y = 3 e^{3 t} - 2 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 3 e^{3 t} - 2 e^{- 3 t}

y = 3 e^{3 t} - 2 e^{- 3 t}

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

y^{^{''}} + 4 y = 0, y^{0} = 1

- y^{^{''}} + 2 y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 2

x^{^{''}} + 2 x^{^{'}} + x = 0, x (0) = 0, x^{^{'}} (0) = 1

x^{^{''}} + 28 x^{^{'}} + 196 x = 0

What is the solution for y^{''}-9y=0,y(0)=1,y^'(0)=15 ?
The solution for y^{''}-9y=0,y(0)=1,y^'(0)=15 is y=3e^{3t}-2e^{-3t}