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

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

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

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

y = \frac{e ^{3 t} ( - 6 + 2 c _{2} )}{3} + c_{2} e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = \frac{e ^{3 t} ( - 6 + 2 c _{2} )}{3} + c_{2} e^{- 2 t}

y = \frac{e ^{3 t} ( - 6 + 2 c _{2} )}{3} + c_{2} e^{- 2 t}

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