What is the solution for 2x^{''}+5x^'+2x=10sin(t) ?

The solution for 2x^{''}+5x^'+2x=10sin(t) is x=c_{1}e^{-t/2}+c_{2}e^{-2t}-2cos(t)

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2x^{''}+5x^'+2x=10sin(t)

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 10 sin (t)

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - 2 cos (t)

Solution steps

2 x^{''} (t) + 5 x^{'} (t) + 2 x = 10 sin (t)

Solve linear ODE:

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - 2 cos (t)

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - 2 cos (t)

What is the solution for 2x^{''}+5x^'+2x=10sin(t) ?
The solution for 2x^{''}+5x^'+2x=10sin(t) is x=c_{1}e^{-t/2}+c_{2}e^{-2t}-2cos(t)