What is the solution for y^{''}-4y^'-13y=0 ?

The solution for y^{''}-4y^'-13y=0 is y=c_{1}e^{(2+sqrt(17))t}+c_{2}e^{(2-sqrt(17))t}

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y^{''}-4y^'-13y=0

y^{^{''}} - 4 y^{^{'}} - 13 y = 0

y = c_{1} e^{(2 + 17) t} + c_{2} e^{(2 - 17) t}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 13 y = 0

Solve linear ODE:

y = c_{1} e^{(2 + 17) t} + c_{2} e^{(2 - 17) t}

y = c_{1} e^{(2 + 17) t} + c_{2} e^{(2 - 17) t}

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0, x (0) = - \frac{1}{2}

y^{^{''}} - 16 y^{^{'}} + 73 y = 0

y^{^{''}} - 8 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

- y^{^{'''}} - y = 0

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

What is the solution for y^{''}-4y^'-13y=0 ?
The solution for y^{''}-4y^'-13y=0 is y=c_{1}e^{(2+sqrt(17))t}+c_{2}e^{(2-sqrt(17))t}