What is the solution for y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1 ?

The solution for y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1 is y=2e^{4t}+3e^{-3t}

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y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 5, y^{^{'}} (0) = - 1

y = 2 e^{4 t} + 3 e^{- 3 t}

Solution steps

y^{''} (t) - y^{'} (t) - 12 y = 0

Solve linear ODE:

y = 2 e^{4 t} + 3 e^{- 3 t}

y = 2 e^{4 t} + 3 e^{- 3 t}

y^{^{''}} + 11 y^{^{'}} + 30 y = 0

x^{^{''}} + 5 x^{^{''}} + 6 x = 0

y^{^{''''}} - 2 y^{^{'''}} - 7 y^{^{''}} = 0

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} - 20 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y (0) = - 3

What is the solution for y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1 ?
The solution for y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1 is y=2e^{4t}+3e^{-3t}