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

The solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 is y=(1-5/7)e^{4t}+5/7 e^{-3t}

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

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

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

What is the solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 ?
The solution for y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-1 is y=(1-5/7)e^{4t}+5/7 e^{-3t}