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

The solution for y^{''}-6y^'+5y=0,y(0)=5,y^'(0)=-6 is y=(5-31/4)e^{5t}+31/4 e^t

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

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

y = (5 - \frac{31}{4}) e^{5 t} + \frac{31}{4} e^{t}

Solution steps

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

Solve linear ODE:

y = (5 - \frac{31}{4}) e^{5 t} + \frac{31}{4} e^{t}

y = (5 - \frac{31}{4}) e^{5 t} + \frac{31}{4} e^{t}

y^{^{''}} + k^{2} y^{^{'}} = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = - 4, y^{^{'}} (0) = 26

(d^{2} + 1)^{2} y = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 3 x^{4}

8 y^{^{''}} + 64 y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

What is the solution for y^{''}-6y^'+5y=0,y(0)=5,y^'(0)=-6 ?
The solution for y^{''}-6y^'+5y=0,y(0)=5,y^'(0)=-6 is y=(5-31/4)e^{5t}+31/4 e^t