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

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

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y^{'''}-5y^{''}+3y^'+y=0

y^{^{'''}} - 5 y^{^{''}} + 3 y^{^{'}} + y = 0

y = c_{1} e^{t} + c_{2} e^{(2 + 5) t} + c_{3} e^{(2 - 5) t}

Solution steps

y^{'''} (t) - 5 y^{''} (t) + 3 y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{(2 + 5) t} + c_{3} e^{(2 - 5) t}

y = c_{1} e^{t} + c_{2} e^{(2 + 5) t} + c_{3} e^{(2 - 5) t}

64 y^{^{''}} + 112 y^{^{'}} + 49 y = 0

\frac{1}{16} x^{^{''}} + 2 x^{^{'}} + x = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 10

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (π) = - 1, y (0) = 1

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = 7

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