What is the solution for y^{''}-2y^'-10y=0 ?

The solution for y^{''}-2y^'-10y=0 is y=c_{1}e^{(1+sqrt(11))t}+c_{2}e^{(1-sqrt(11))t}

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y^{''}-2y^'-10y=0

y^{^{''}} - 2 y^{^{'}} - 10 y = 0

y = c_{1} e^{(1 + 11) t} + c_{2} e^{(1 - 11) t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{(1 + 11) t} + c_{2} e^{(1 - 11) t}

y = c_{1} e^{(1 + 11) t} + c_{2} e^{(1 - 11) t}

0.5 y^{^{''}} + y^{^{'}} + 10 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + \frac{a}{4} y = 0, y^{^{'}} (π) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 2 x^{^{'}} + 10 x = 0, x (0) = 1, x^{^{'}} (0) = 0

4 y^{^{''}} + \frac{16}{0.25} y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{16}{32} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 2, x^{^{'}} (0) = 1

What is the solution for y^{''}-2y^'-10y=0 ?
The solution for y^{''}-2y^'-10y=0 is y=c_{1}e^{(1+sqrt(11))t}+c_{2}e^{(1-sqrt(11))t}