What is the solution for q^{''}+100q^'+2500q=30,q(0)=0,q(0)=2 ?

The solution for q^{''}+100q^'+2500q=30,q(0)=0,q(0)=2 is q(t)=-3/250 e^{-50t}+c_{2}e^{-50t}t+3/250

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q^{''}+100q^'+2500q=30,q(0)=0,q(0)=2

q^{^{''}} + 100 q^{^{'}} + 2500 q = 30, q (0) = 0, q (0) = 2

q (t) = - \frac{3}{250} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{3}{250}

Solution steps

q^{''} (t) + 100 q^{'} (t) + 2500 q (t) = 30

Solve linear ODE:

q (t) = - \frac{3}{250} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{3}{250}

q (t) = - \frac{3}{250} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{3}{250}

(D^{3} + D) y = e^{- 2 x} cos (2 x)

x^{^{''}} + 2.5 x^{^{'}} + 50 x = 1.5 cos (t)

y^{^{''}} + 4 y = g (t), y (0) = 6, y^{^{'}} (0) = 18

y^{^{''}} - 4 y = 1 - cos (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 36 y = sin (7 x), y (0) = 0, y^{^{'}} (0) = 0

What is the solution for q^{''}+100q^'+2500q=30,q(0)=0,q(0)=2 ?
The solution for q^{''}+100q^'+2500q=30,q(0)=0,q(0)=2 is q(t)=-3/250 e^{-50t}+c_{2}e^{-50t}t+3/250