What is the solution for y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1 ?

The solution for y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1 is y=-3e^{3t}+4e^{2t}

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y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 9 y^{^{''}} + 19 y^{^{'}} + 11 y = 0

y^{^{''}} = 5 y^{^{'}}

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} + a^{2} \cdot y = 0

y^{^{''}} - 16 y^{^{'}} + 64 y = 0, y (0) = 2

What is the solution for y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1 ?
The solution for y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1 is y=-3e^{3t}+4e^{2t}