What is the solution for y^{''}+10y^'+23y=0 ?

The solution for y^{''}+10y^'+23y=0 is y=c_{1}e^{(-5+sqrt(2))t}+c_{2}e^{(-5-sqrt(2))t}

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y^{''}+10y^'+23y=0

y^{^{''}} + 10 y^{^{'}} + 23 y = 0

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

Solution steps

y^{''} (t) + 10 y^{'} (t) + 23 y = 0

Solve linear ODE:

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

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

4 \frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + 9 y = 0

y^{^{''}} - 6 y^{^{'}} + 5 y = 0

2 y^{^{''}} + 4 y^{^{'}} + 7 y = 0

x^{^{''}} + 9 x = 0, x^{^{'}} (0) = 4, x (0) = 3

y^{^{''}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 22

What is the solution for y^{''}+10y^'+23y=0 ?
The solution for y^{''}+10y^'+23y=0 is y=c_{1}e^{(-5+sqrt(2))t}+c_{2}e^{(-5-sqrt(2))t}