# Solving System of Differential Equations with initial conditions maple

I've been asked to solve a system of differential equations using maple (for practice, as it is solvable by hand...), but I seem to be running into goop with syntax...

d/dt r(t) = -lambda_r*r(t) + alpha*lambda_u*u

d/dt p(t) = -lambda_p*p(t) + lambda_r * r(t)

with initial conditions r(0) = r_0 and p(0) = p_0

So I put this in maple:

de1 := diff(R(t),t) = -lambda[r]*R(t)+alpha*lambda[u]*U;

de2 := diff(P(t),t) = -lambda[p]*P(t)+lambda[r]*R(t);

Now,

dsol := dsolve({de1, de2}, {R(t), P(t)});

gets me R(t) and P(t) but when do I plug in the initial conditions? Is that afterwards on dsol[1] and dsol[2], or should I be doing that when I do the dsolve somehow?

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What does the included help say? In Maple, type ?dsolve to get it. I would try dsolve({de1, de2, R(0)=r0, P(0)=p0}, {R(t), P(t)}); – GEdgar Feb 23 '13 at 2:26

As GEdgar wrote in the comments, the initial conditions should be included along with the differential equations. Here is an example from Maple help file that you get by entering ? dsolve: