wolfram alpha cannot solve some problems

[drhu...@gmail.com]

wolfram alpha cannot solve some problems in http://12000.org/my_notes/kamek/kamke_differential_equations.htm which are mark as solved in mathematica but its solution are very complicated so it cannot check if it is right answer or not. e. g. problems ode No 64-73, 84.


mathHandbook.com can give simple solution so it is easy to check the answer. it can solve some problems that Mathematica cannot. just copy maple input to mathHandbook.com, then hit the ENTER key in your keyboard.

www.mathHandbook.com

[drhu...@gmail.com]

y’=sin(x-y) has very simple solution but wolfram give very complicated solution. why?

mathHand.com give a simple solution
http://server.drhuang.com/input/?guess=dsolve%28y%281%2Cx%29%3Dsin%28x-y%29%29&inp=y%281%2Cx%29%3Dsin%28x-y%29&lang=null

[drhu...@gmail.com]

Wolfram and wolframcloud cannot solve a simple equation y’=4sin(y-x)-4
one click to solve it in mathHand.com
http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Cx%2C2%29%2B2ds%28y%29%2By%3D0%29&inp=ds%28y%2Cx%2C2%29%2B2ds%28y%29%2By%3D0&lang=null

[Dr Huang]

On Saturday, 9 January 2021 at 12:35:14 UTC+11, drhu...@gmail.com wrote:
> On Friday, 8 January 2021 at 10:36:30 UTC+11, drhu...@gmail.com wrote:
> > On Thursday, 7 January 2021 at 23:45:38 UTC+11, drhu...@gmail.com wrote:
> > > On Thursday, 7 January 2021 at 23:28:50 UTC+11, drhu...@gmail.com wrote:
> > > > On Thursday, 7 January 2021 at 13:30:51 UTC+11, Nasser M. Abbasi wrote:
> > > > > >
> > > > > > why wolfram cannot find simple solution in many equations? many examples, e.g.:
> > > > > > 1/x*y"-y-x^2=0
> > > > > > 1/x*y"-y-x^3=0
> > > > > > 1/x*y"-y-x^4=0
> > > > > > ......
> > > > > >
> > > > > > mathHand.com can:
> > > > > > http://server.drhuang.com/input/?guess=dsolve%281%2Fx*ds%28y%2Cx%2C2%29-y-x%5E3%29
> > > > > >
> > > > > > so it is good idea to use two software to check solution.
> > > > > >
> > > > > For the first ode above. This is inhomogeneous Airy ode. The solution you give for
> > > > >
> > > > > 1/x*y''[x]-y[x]-x^2==0
> > > > >
> > > > > is
> > > > >
> > > > > y(x)= -6+Ai(x)*C1+Bi(x)*C2-x^3
> > > > >
> > > > > But this solution is not verified by Maple:
> > > > >
> > > > > ==============
> > > > > restart;
> > > > > ode := 1/x*diff(y(x),x$2) - y(x) - x^2 = 0;
> > > > > sol := y(x) = -6+AiryAi(x)*_C2 + AiryBi(x)*_C1-x^3;
> > > > > odetest(sol,ode);
> > > > >
> > > > > x^3 - x^2
> > > > > =================
> > > > >
> > > > > Which is not zero. Hence not a valid solution?
> > > > >
> > > > > --Nasser
> > > > the bug fixed. thanks.
> > > > mathHand.com
> > > input your equation into mathHand.com, click the "dsolve" button to solve, then click the "test" button to test its solution, or click the "to inte" button to plot if it did not auto plot.
> > >
> > > http://mathHand.com
> > wolfram gives very complicated solution:
> > y"-x y-x^3+2=0
> > mathHand.com gives very simple solution:
> > http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Cx%2C2%29-x*y-x%5E3%2B2%29
>
> wolfram gives very complicated solution:
> y"-x y'-x y-x^3+2=0
> mathHand.com gives very simple solution:
> http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Cx%2C2%29-ds%28y%2Cx%2C1%29*x-y*x-x%5E3%2B2%29&inp=ds%28y%2Cx%2C2%29-ds%28y%2Cx%2C1%29*x-y*x-x%5E3%2B2


Wolfram cannot find simple solution but mathHand.com can in following equations:
y"-x*y'-x*y-x=0
y"-x*y'-x*y-x^2=0
y"-x*y'-x*y-x^3+2=0
y"-x*y'-x*y-x^4-6=0
y"-x*y'-x*y-x^5+12=0
y"-x*y'-x*y-x^n=0, where n=1,2,3 ......
y"-a*x*y'-b*x*y-c*x^n=0, where n=1,2,3 ......
y"-y'-x*y-x=0
y"-y'-x*y-x^2=0
y"-y'-x*y-x^2-1=0
y"-2*y'-x*y-x^2-2=0
y"-4*y'-x*y-x^2-4=0
y"-y'-x*y-x^n=0, where n=1,2,3......
y"-a*y'-b*x*y-c*x^n=0, where n=1,2,3 ......
y"-x*y-x^3+2=0
y"-x*y-x^6+40=0
y"-x*y-x^n=0, where n=1,2,3 ......
......
more examples in
http://drhuang.com/science/mathematics/fractional_calculus/fractional_differential_equation.htm