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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

2 x^{^{''}} + 2 x^{^{'}} + 7 x = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 20, y^{^{'}} (0) = 0

x^{^{''}} + 6 x^{^{'}} + 13 x = 0

c y^{^{''}} + ab y^{^{'}} = 0

3 y^{^{''}} + 35 y = 0, y (0) = 2, y^{^{'}} (0) = 9

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