What is the solution for y^{''}-5y^'-6y=0,y^'(0)=4,y^'(0)=-4 ?

The solution for y^{''}-5y^'-6y=0,y^'(0)=4,y^'(0)=-4 is y=(e^{6t}(4+c_{2}))/6+c_{2}e^{-t}

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y^{''}-5y^'-6y=0,y^'(0)=4,y^'(0)=-4

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y^{^{'}} (0) = 4, y^{^{'}} (0) = - 4

y = \frac{e ^{6 t} ( 4 + c _{2} )}{6} + c_{2} e^{- t}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 6 y = 0

Solve linear ODE:

y = \frac{e ^{6 t} ( 4 + c _{2} )}{6} + c_{2} e^{- t}

y = \frac{e ^{6 t} ( 4 + c _{2} )}{6} + c_{2} e^{- t}

y^{^{''}} + 5 y^{^{'}} + 14 y = 0

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

y^{^{''}} + 50 y = 0

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

2 x^{^{''}} + 8 x^{^{'}} + 52 x = 0

What is the solution for y^{''}-5y^'-6y=0,y^'(0)=4,y^'(0)=-4 ?
The solution for y^{''}-5y^'-6y=0,y^'(0)=4,y^'(0)=-4 is y=(e^{6t}(4+c_{2}))/6+c_{2}e^{-t}