why wolframe cannot find simple solution?

[Dr Huang]

On Friday, 11 December 2020 at 10:13:09 UTC+11, drhu...@gmail.com wrote:
> why wolfram cannot find simple solution in many equations? These equations have a very simple solution. e.g.
> d^2/dx^2-dy/dx *x-y*x-x^2=0
> Click the dsolve button to solve it, then click the test button to test its solution in mathHand.com.
> http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Cx%2C2%29-ds%28y%29*x-x*y-x%5E2%29&inp=ds%28y%2Cx%2C2%29-ds%28y%29*x-x*y-x%5E2

why wolfram cannot find simple solution in many equations? many examples, e.g.:
x*y"-y-x^2=0
x*y"-y-x^3=0
x*y"-y-x^4=0
......

mathHand.com can:
http://server.drhuang.com/input/?guess=dsolve%28x*ds%28y%2Cx%2C2%29-y-x%5E2%29

http://server.drhuang.com/input/?guess=dsolve%28x*ds%28y%2Cx%2C2%29-y-x%5E3%29

[Dr Huang]

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.

[Dr Huang]

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

[Dr Huang]

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

[Dr Huang]

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

[Dr Huang]

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 ......
......

http://drhuang.com/science/mathematics/fractional_calculus/fractional_differential_equation.htm

[Dr Huang]

more and more examples are in
http://drhuang.com/science/mathematics/fractional_calculus/fractional_differential_equation.htm

[Kristjan Robam]

(_!_)

[Dr Huang]

more examples are in http://drhuang.com/index/bug