What is the solution for 1/2 x^{''}+3/2 x^'+x=0 ?

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

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1/2 x^{''}+3/2 x^'+x=0

\frac{1}{2} x^{^{''}} + \frac{3}{2} x^{^{'}} + x = 0

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

Solution steps

\frac{1}{2} x^{''} (t) + \frac{3}{2} x^{'} (t) + x = 0

Solve linear ODE:

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

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

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