Re: DSolve validation
- To: mathgroup at smc.vnet.net
- Subject: [mg33996] Re: DSolve validation
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 26 Apr 2002 03:27:15 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <aa8b0q$hbs$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, > Life is great! Inspirited with the success, let's consider this ODE. > > In[4] := ode1 = y''[x] + x y[x] == 0; > > In[5] := sol1 = DSolve[ode1, y[x], x] > Out[5] = {{y[x] -> AiryAi[(-1)^(1/3)*x]*C[1] + AiryBi[(-1)^(1/3)*x]*C[2]}} > > In[6] := ode1 /. D[sol1, x, x] /. D[sol1, x] > Out[6] = {{-(x*AiryAi[(-1)^(1/3)*x]*C[1]) - x*AiryBi[(-1)^(1/3)*x]*C[2] + x*y[x] == 0}} > > (* Oops! The trick does not work ;-( *) > > In[7] := ode1 /. D[sol1, x, x] /. D[sol1, x]//FullSimplify > Out[7] = {{x*(AiryAi[(-1)^(1/3)*x]*C[1] + AiryBi[(-1)^(1/3)*x]*C[2] - y[x]) == 0}} > > (* Not great, again *) > > In[8] := ode1 /. D[sol1, x, x] /. D[sol1, x] // ComplexExpand // FullSimplify > Out[8] = {{x*(AiryAi[(-1)^(1/3)*x]*C[1] + AiryBi[(-1)^(1/3)*x]*C[2] - y[x]) == 0}} > > (* etc etc etc *) > > > 'Fraid, the same double check trouble holds for the hundreds ODEs I have tried 8-( > > What might be a more or less streamlined way to validate the DSolve solutions? Insert the solution ? and not only the derivatives ? Try: ode1 /. sol1 /. D[sol1, x, x] /. D[sol1, x] // FullSimplify Regards Jens