DSolveConstants problem

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1141] DSolveConstants problem*From*: rich_klopp at qm.sri.com (Richard W. Klopp)*Date*: Wed, 17 May 1995 04:19:21 -0400*Organization*: SRI International

I am (still) having problems with DSolve. As you will see at In[8]: below, the kernel is brought to its knees when I try to define the integration constants to be something other than the default C[i]. I am running version 2.2.2 on a PowerMac 7100/66 and have allocated 5 Megs to the kernel. In[1]:=<<Calculus`DSolve` Define a nonlinear ODE: In[2]:= r[z] := a z^2 + g In[3]:= leftside1 = (r[z]^2 + e) D[u[z],{z,2}] + D[r[z]^2,z] D[u[z],z]; In[4]:= eq1 = (leftside1 == 0) Out[4]= 2 2 2 4 a z (g + a z ) u'[z] + (e + (g + a z ) ) u''[z] == 0 Solve the ODE and time how long it takes. In[5]:= Timing[DSolve[eq1, u[z],z]] Out[5]= {26.35 Second, {{u[z] -> 1 C[2] + C[1] Integrate[-------------------------, z]}} 2 2 2 4 e + g + 2 a g z + a z } Let's define the same ODE with a new dependent variable. In[6]:= leftside2 = (r[z]^2 + e) D[v[z],{z,2}] + D[r[z]^2,z] D[v[z],z]; In[7]:= eq2 = (leftside2 == 0) Out[7]= 2 2 2 4 a z (g + a z ) v'[z] + (e + (g + a z ) ) v''[z] == 0 Solve the new ODE and time how long it takes. ***Use a different, non-default integration constant this time.*** In[8]:= Timing[DSolve[eq2, v[z],z,{DSolveConstants->b}]] ******After 15 minutes, I give up! What's wrong here?******* Out[8]= $Aborted Let's do a simpler problem to make sure we've got the DSolveConstants syntax right. In[9]:= eq3 = ( D[w[z],{z,2}] == -2 T ) Out[9]= w''[z] == -2 T In[10]:= DSolve[eq3,w[z],z,{DSolveConstants -> f}] Out[10]= 2 {{w[z] -> -(T z ) + f[1] + z f[2]}} Looks like the syntax is correct. Let's time it, and the default version. In[11]:= Timing[DSolve[eq3,w[z],z,{DSolveConstants -> f}]] Out[11]= 2 {0.116667 Second, {{w[z] -> -(T z ) + f[1] + z f[2]}}} In[12]:= Timing[DSolve[eq3,w[z],z]] Out[12]= 2 {0.266667 Second, {{w[z] -> -(T z ) + C[1] + z C[2]}}} So, what's the problem at In[8]:? I want to define different constants because I want to solve several similar ODEs and keep their integration constants separate. Thanks for your help, Rich Klopp rich_klopp at qm.sri.com