What is the solution for 5x^{''}+10x^'+30x=300 ?

The solution for 5x^{''}+10x^'+30x=300 is x=e^{-t}(c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t))+10

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5x^{''}+10x^'+30x=300

5 x^{^{''}} + 10 x^{^{'}} + 30 x = 300

x = e^{- t} (c_{1} cos (5 t) + c_{2} sin (5 t)) + 10

Solution steps

5 x^{''} (t) + 10 x^{'} (t) + 30 x = 300

Solve linear ODE:

x = e^{- t} (c_{1} cos (5 t) + c_{2} sin (5 t)) + 10

x = e^{- t} (c_{1} cos (5 t) + c_{2} sin (5 t)) + 10

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

- y^{^{''}} + y^{^{'}} + 6 y = 1 - x

y^{''} - 3 y^{'} + 2 y = 1 1^{(e^{3} x)}

y^{^{''}} - 2 y^{^{'}} + y = \frac{3 e ^{t}}{t ^{2} + 1}

y^{^{''}} - 36 y = 180 t - 72 e^{- 1}, y (0) = 0, y^{^{'}} (0) = 61

What is the solution for 5x^{''}+10x^'+30x=300 ?
The solution for 5x^{''}+10x^'+30x=300 is x=e^{-t}(c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t))+10