What is the solution for y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=1 ?

The solution for y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=1 is y=(3-7/2)e^{5t}+7/2 e^t

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y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y = (3 - \frac{7}{2}) e^{5 t} + \frac{7}{2} e^{t}

Solution steps

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

Solve linear ODE:

y = (3 - \frac{7}{2}) e^{5 t} + \frac{7}{2} e^{t}

y = (3 - \frac{7}{2}) e^{5 t} + \frac{7}{2} e^{t}

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

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

What is the solution for y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=1 ?
The solution for y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=1 is y=(3-7/2)e^{5t}+7/2 e^t