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I have to find

1.the complementary function, particular integral and the general solution.

2. find complete solution when t=0, q=0, dq/dt=0.

-equation 2(d^2q)/(dt^2)+200dq/dt+5000q = 250

-in D operator form it looks like (2D^2+200d+5000)y=250

- subsituting m for D i receve repeated root m= -50

- so the complemenary function (At+B)e^(-50t)

- right side is constant so i subsituted constant into equation and solved that k= 0.05

- so the general solution is q=(At+B)e^(-50t)+0.05 right??

Now when t=0. q=0 , dq/dt=0

1) 0 = (A(0)+B)e^0+0.05

B= -0.05

And now i have problem

2) dq/dt= -50(At+B)e^(-50t) what the solution should be. I should find A but it dissapears because of t=0

I have no idea what to do with it.