What is the solution for y^{''}-5y^'+4y=0,y(0)=-3,y^'(0)=3 ?

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

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y^{''}-5y^'+4y=0,y(0)=-3,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - 3, y^{^{'}} (0) = 3

y = 2 e^{4 t} - 5 e^{t}

Solution steps

y^{''} (t) - 5 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 2 e^{4 t} - 5 e^{t}

y = 2 e^{4 t} - 5 e^{t}

y^{^{''}} + 12 y^{^{'}} - 27 y = 0

16 y - 8 y^{^{'}} = - y^{^{''}}

8 y^{^{''}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

y^{^{''}} = - y

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = - 3

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