What is the solution for 1/4 x^{''}-x=0,x(0)=1,x^'(0)=5 ?

The solution for 1/4 x^{''}-x=0,x(0)=1,x^'(0)=5 is x=(1+3/4)e^{2t}-3/4 e^{-2t}

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1/4 x^{''}-x=0,x(0)=1,x^'(0)=5

\frac{1}{4} x^{^{''}} - x = 0, x (0) = 1, x^{^{'}} (0) = 5

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

Solution steps

\frac{1}{4} x^{''} (t) - x = 0

Solve linear ODE:

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

What is the solution for 1/4 x^{''}-x=0,x(0)=1,x^'(0)=5 ?
The solution for 1/4 x^{''}-x=0,x(0)=1,x^'(0)=5 is x=(1+3/4)e^{2t}-3/4 e^{-2t}