What is the solution for 5/6 q^{''}+10q^'+60q=600 ?

The solution for 5/6 q^{''}+10q^'+60q=600 is q(t)=e^{-6t}(c_{1}cos(6t)+c_{2}sin(6t))+10

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5/6 q^{''}+10q^'+60q=600

\frac{5}{6} q^{^{''}} + 10 q^{^{'}} + 60 q = 600

q (t) = e^{- 6 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + 10

Solution steps

\frac{5}{6} q^{''} (t) + 10 q^{'} (t) + 60 q (t) = 600

Solve linear ODE:

q (t) = e^{- 6 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + 10

q (t) = e^{- 6 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + 10

\frac{d ^{2} y}{d t ^{2}} - 4 y = t cos (2 t), t = 0

x^{^{''}} + \frac{1.0889}{19.6} x = cos (2 t)

0.001 y^{^{''}} + 10 y = 10 cos (100 x)

y^{^{''}} + 2 y^{^{'}} + y = (1 + x) e^{- x}

(D^{2} - 2 D + 1) y = x sin (x)

What is the solution for 5/6 q^{''}+10q^'+60q=600 ?
The solution for 5/6 q^{''}+10q^'+60q=600 is q(t)=e^{-6t}(c_{1}cos(6t)+c_{2}sin(6t))+10