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>
• 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

```

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