# Question:How do I solve a first order linear PDE with two time dependent variables? (physics, Hamiltonian eqns, probability density)

## Question:How do I solve a first order linear PDE with two time dependent variables? (physics, Hamiltonian eqns, probability density)

Maple 16

Hello!

For the last couple of days I've been trying really hard to solve the linear PDE

. Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=   .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D).

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given".

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple?

Thankful for any help

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