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