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Question: differential equation with two solutions

Question:differential equation with two solutions

kh2n 220 Maple
October 25 2010
0



> 

restart:
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ode:=k_m*diff(T(x),x,x)+cp*m_v*diff(T(x),x)=0;

(1)
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ics:=D(T)(0)=-q/k_m,T(L)=TV;

(2)
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dsolve({ode,ics});

(3)
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simplify(%, trig):
  combine(%, exp) assuming S::real:
  collect(%,q):collect(%,cp):collect(%,m_v):                                                                                                        simplify(%, size) assuming S::real;

(4)

 If I change just only one sign from positive to negative in the above solution (4) which will now take the following form

> 

T(x):= TV-(-exp(-cp*m_v/k_m*L)+exp(-cp*m_v/k_m*x))*q/cp/m_v;

(5)
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I have checked it that both the soltuions satisfy the differential equation. Now my question is, can the second solution (5) in which I have only change one sign from positive to negitive is correct?

If both the solution are correct then what is the best way to get more solutions of a differential equation of there is more then one solution.  



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