From: drhuang57@gmail.com   
      
   On Sunday, 26 November 2023 at 14:25:30 UTC+11, Dr Huang (DrHuang.com) wrote:   
   > On Sunday, 26 November 2023 at 01:13:11 UTC+11, Nasser M. Abbasi wrote:   
   > > On 11/25/2023 6:03 AM, Dr Huang (DrHuang.com) wrote:   
   > >   
   > > > Any CAS around that can show me a trend of y'-exp(y)-x-x*x=0 ?   
   > > I have no idea what "trend" of an ode mean. This is a new   
   > > term for me that I still have not learned at school and   
   > > first time I see it.   
   > I think it is graphic solution.   
   > >   
   > > But if you just mean the solution of the ode, this is an   
   > > easy ode to solve. Just use the substitution u=exp(-y)   
   > > which converts it to linear first order ode in u(x) which   
   > > is solved using an integrating factor.   
   > >   
   > > Here is my solution attached with slope field plot.   
   > >   
   > > https://12000.org/tmp/solved_problems/nov_25_2023.pdf   
   > >   
   > > The only issue is that there remain unresolved integral.   
   > >   
   > > int( exp(1/3*x^3+1/2*x^2), x)   
   > >   
   > > Which could not be solved by Maple nor Mathematica nor Rubi so the   
   > > solution has this unresolved integral in it.   
   > mathHand.com found it with http://server.drhuang.com/input/?gu   
   ss=dsolve(y(1,x)-exp(y)-x-x*x=0) &   
   http://server.drhuang.com/input/?guess=dsolve(y(1,x)-exp(y)-x-x*x=0)&   
      
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