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I need to solve a system of differential equations as follows:

Clear[t]

system =
  { x'[t] ==  2.2758*y[t] - x[t]/200, 
    y'[t] == - 2*2.2758*E^(-(0.7071^2))*E^(-((1.77*t)^2/13.8^2))*Cos[-0.5*t]*z[t]
             + 2.2758*x[t]  - y[t]/200, 
    z'[t] == 2*2.2758*E^(-(0.7071^2))*E^(-((1.77*t)^2/13.8^2))*Cos[-0.5*t]*y[t]};
initialvalues = {x[0] ==  0, y[0] ==  0, z[0] ==  -1};

sol = DSolve[ Join[ system, initialvalues], {x, y, z}, t]

Unfortunately, Mathematica is not able to yield a result. Is there a way to do it?

Also I have another question. I want to make the values of x , y and z be numbers (numerical values) at t == 0. How I can do that ?

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marked as duplicate by m_goldberg, Sjoerd C. de Vries, Artes, Michael E2, belisarius Oct 28 '13 at 4:41

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
Working with DSolve you should replace machine precission numbers by exact ones. See a related problem here: No result while try to DSolve. –  Artes Oct 27 '13 at 13:12

1 Answer 1

You can solve your problem numerically by switching to NDSolve and providing limits for t:

sol = NDSolve[Join[system, initialvalues], {u, v, w}, {t, -20, 0}]
Plot[{u[t], v[t], w[t]} /. sol, {t, -20, 0}]

enter image description here

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