What is the solution for x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13 ?

The solution for x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13 is x=(1-11/6)e^{-2t}+11/6 e^{-8t}

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x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13

x^{^{''}} + 10 x^{^{'}} + 16 x = 0, x (0) = 1, x^{^{'}} (0) = - 13

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

Solution steps

x^{''} (t) + 10 x^{'} (t) + 16 x = 0

Solve linear ODE:

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

4 y^{^{''}} + 8 y^{^{'}} - 21 y = 0

6 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = e^{\frac{x}{2}}

y^{^{'''}} + 25 y^{^{'}} = 0

y^{^{'''}} + 2 y^{^{''}} - 20 y^{^{'}} + 24 y = 0

0.25 y^{^{''}} + 10 y^{^{'}} + 1000 y = 0

What is the solution for x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13 ?
The solution for x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13 is x=(1-11/6)e^{-2t}+11/6 e^{-8t}