What is the solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=27 ?

The solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=27 is y=6e^{2t}-5e^{-3t}

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y^{''}+y^'-6y=0,y(0)=1,y^'(0)=27

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 27

y = 6 e^{2 t} - 5 e^{- 3 t}

Solution steps

y^{''} (t) + y^{'} (t) - 6 y = 0

Solve linear ODE:

y = 6 e^{2 t} - 5 e^{- 3 t}

y = 6 e^{2 t} - 5 e^{- 3 t}

y^{^{''}} - 4 y^{^{'}} + 68 y = 0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 17 y = 0

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = 17

y^{^{''}} - y^{^{'}} = y

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 5

What is the solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=27 ?
The solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=27 is y=6e^{2t}-5e^{-3t}