# DSolve to solve a system of differential equations [duplicate]

This question already has an answer here:

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, y ==  0, z ==  -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 ?

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

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