What is the solution for x^{''}+8x^'+15x=0 ?

The solution for x^{''}+8x^'+15x=0 is x=c_{1}e^{-3t}+c_{2}e^{-5t}

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x^{''}+8x^'+15x=0

x^{^{''}} + 8 x^{^{'}} + 15 x = 0

x = c_{1} e^{- 3 t} + c_{2} e^{- 5 t}

Solution steps

x^{''} (t) + 8 x^{'} (t) + 15 x = 0

Solve linear ODE:

x = c_{1} e^{- 3 t} + c_{2} e^{- 5 t}

x = c_{1} e^{- 3 t} + c_{2} e^{- 5 t}

y^{^{''}} + 16 y^{^{'}} = 0, y (0) = 2, y^{^{'}} (0) = - 2

y^{^{'''}} + 7 y^{^{''}} - 17 y^{^{'}} + 9 y = 0

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

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

y^{^{''}} + 3 y + 2 y = 0

What is the solution for x^{''}+8x^'+15x=0 ?
The solution for x^{''}+8x^'+15x=0 is x=c_{1}e^{-3t}+c_{2}e^{-5t}