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Original Message (ID '101677') By Bill Simpson:
If I understand correctly then your differential equation appears simple enough to directly solve. In[1]:=\[CapitalGamma]=0; \[CapitalDelta]=0; OBE={Dt[u[t],t]==\[CapitalDelta]/\[CapitalOmega] v[t]-\[CapitalGamma]/(2 \[CapitalOmega]) u[t],Dt[v[t],t]\[Equal]-(\[CapitalDelta]/\[CapitalOmega]) u[t]+w[t]-\[CapitalGamma]/(2 \[CapitalOmega]) v[t],Dt[w[t],t]\[Equal]-v[t]-\[CapitalGamma]/\[CapitalOmega] (w[t]-1),u[0]==0,v[0]==0,w[0]==1}; s=DSolve[OBE,{u[t],v[t],w[t]},t]; First[{u[t],v[t],w[t]}/.s] Out[5]= {0,Sin[t],Cos[t]} and you can use that in your Manipulate.