From: drhuang57@gmail.com   
      
   On Saturday, 21 October 2023 at 07:56:13 UTC+11, Mild Shock wrote:   
   > 1) Here Wolfram Alpha can show me a trend:   
   > Problem:   
   > y' = cos(t) * (2 + cos(t)) / 100   
   > Solution:   
   > y(t) = c_1 + t/200 + sin(t)/50 + 1/200 sin(t) cos(t)   
   >   
   > The trend is the linear non-periodic part t/200.   
   >   
   > 2) But here Wolfram Alpha fails to show me a trend:   
   > Problem (real valued root):   
   > y' = cos(t)^(1/3) * (2 + cos(t)) / 100   
   > Solution:   
   > y(t) = c_1   
   > - 3/200 sqrt(sin^2(t)) cos(t)^(1/3) cot(t)   
   > 2F1(1/2, 2/3, 5/3, cos^2(t))   
   > - 3/700 sqrt(sin^2(t)) cos(t) cos(t)^(1/3) cot(t)   
   > 2F1(1/2, 7/6, 13/6, cos^2(t))   
   >   
   > Doesn't show me a linear non-period part,   
   > but I guess it has one.   
   >   
   > Any CAS around that can show me a trend?   
   mathHandbook.com can solve eq and auto plot its solution if variable is x, for   
   your example   
   http://server.drhuang.com/input/?guess=dsolve%28y%27+%3D+cos%28x   
   29%5E%281%2F3%29+*+%282+%2B+cos%28x%29%29+%29&inp=y%27+%3D+cos%2   
   x%29%5E%281%2F3%29+*+%282+%2B+cos%28x%29%29+&lang=en   
      
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