What is the solution for y^{''}-5y^'+4y=0,y(0)=5,y^'(0)=8 ?

The solution for y^{''}-5y^'+4y=0,y(0)=5,y^'(0)=8 is y=e^{4t}+4e^t

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y^{''}-5y^'+4y=0,y(0)=5,y^'(0)=8

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 8

y = e^{4 t} + 4 e^{t}

Solution steps

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

Solve linear ODE:

y = e^{4 t} + 4 e^{t}

y = e^{4 t} + 4 e^{t}

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

y^{^{''}} - 36 y = 0, y (0) = 1

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

y^{^{'''}} + 12 y^{^{''}} + 45 y^{^{'}} = 0

What is the solution for y^{''}-5y^'+4y=0,y(0)=5,y^'(0)=8 ?
The solution for y^{''}-5y^'+4y=0,y(0)=5,y^'(0)=8 is y=e^{4t}+4e^t