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I am new to Maple, trying to see how do I add initial conditions to a system of partial differential equations. Here is an example problem, which has some error in it. What is wrong? This appears on the worksheet:

sys:=$\frac{\partial}{\partial t}f1(x,t)=f2(x,t),\frac{\partial}{\partial x}f2(x,t)=-f1(x,t)$

pdsolve({sys})

yields

$$f1(x,t)=\frac{-C_1 C_2 c_1 e^{c_1 x}}{e^{t/c_1}},f2(x,t)=\frac{C_1 C_2 e^{c_1 x}}{e^{t/c_1}}$$

Trying to add initial conditions:

ics:=$f1(0,0)=-1,f2(0,0)=1$

And then attempting

pdsolve({sys,ics})

doesn't produce an output; No error message or anything... Only the cursor moves to the next line in the worksheet. I checked the solution, the initial conditions are consistent with the solution above and the final solution should have been:

$$f1(x,t)=-e^{x-t},f2(x,t)=e^{x-t}$$

What would be the proper way to do this?

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1 Answer 1

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As it turns out, Maple does not find an unique solution, since other solutions can be shown to exist (such as a sum of cos(x+t) and sin(x+t) multiplied with constants). The reason for this is - in the above exaMPLE, insufficient information HAS been fed into Maple and it cannot produce an unique solution. Adding the initial conditions still permits both the "exp" solutions shown above as well as the sin/cos combination just mentioned.

It appears in such cases Maple bails out, without an output.

Thus, other (initial) conditions are needed to produce an unique solution.

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