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Question: why Maple gives extra solutions to this basic ode?

Question:why Maple gives extra solutions to this basic ode?

nm 10446 Maple 2024
ode dsolve differential-equations
May 24 2024
0

Given the ode   y''(x)*y'(x)=0, clearly it has solutions for y''=0 and y'=0.

These are y=c1+x*c2 and y=c1. But Maple gives 3 solutions

12592

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

ode:=diff(y(x),x$2)*diff(y(x),x)=0;

(diff(diff(y(x), x), x))*(diff(y(x), x)) = 0

> 

dsolve(ode)

y(x) = c__1, y(x) = -c__1*x+c__2, y(x) = c__1*x+c__2

> 

dsolve(diff(y(x),x$2)=0)

y(x) = c__1*x+c__2

> 

dsolve(diff(y(x),x)=0)

y(x) = c__1

 

 

Download why_3_solutions_may_24_2024.mw

Where did the third solution come from? The 3 solutions are correct ofcourse, but why 3? There should only be two. 

FYI, I am using 

Physics:-Version()

The "Physics Updates" version in the MapleCloud is 1746. The 

   version installed in this computer is 1745 created 2024, May 

I have to check earlier Maple versions to see if same thing happens there.
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