Re: DSolve validation

*To*: mathgroup at smc.vnet.net*Subject*: [mg34016] Re: DSolve validation*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Fri, 26 Apr 2002 03:27:50 -0400 (EDT)*Organization*: University of Washington*References*: <aa8b0q$hbs$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Vladimir, You forgot to add the replacement rule sol1 ! So, y[x] was never replaced by the solution. By the way, a simpler way to verify your result is to use DSolve to solve for y and not y[x], as in the following example: ode1 = y''[x] + x*y[x] == 0; sol1 = DSolve[ode1, y, x]; Then, to check your solution all you would need to do is use the replacement rule sol1: In[12]:= FullSimplify[ode1 /. sol1] Out[12]= {True} Carl Woll Physics Dept U of Washington "Vladimir Bondarenko" <vvb at mail.strace.net> wrote in message news:aa8b0q$hbs$1 at smc.vnet.net... > Gentlemen, > > It's easy to double check the DSolve output here: > > In[1] := ode1 = y''[x] + x y'[x] == 0; > > In[2] := sol1 = DSolve[ode1, y[x], x] > Out[2] = {{y[x] -> C[2] + Sqrt[Pi/2]*C[1]*Erf[x/Sqrt[2]]}} > > In[3] := ode1 /. D[sol1, x, x] /. D[sol1, x] > Out[3] = {{True}} > > 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? > Any module (publicly) available? Any (including halp-baked & raw) ideas & hints? > > Thank you a lot for your time and efforts in advance. > > > Sincerely, > > Vladimir Bondarenko > > >