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Question: why dsolve gives numeric exception: division by zero for some coefficients?

Question:why dsolve gives numeric exception: division by zero for some coefficients?

nm 8552 Maple 2020
dsolve differential-equations exception
November 08 2020
4

In this ODE

dsolve gives 

When A=3 but  not when A=1 or A=2

restart;
ode:=(1+y(x))*diff(y(x),x$2)-A*diff(y(x),x)^2=x;
A:=1;
dsolve(ode):
A:=2;
dsolve(ode):
A:=3;
dsolve(ode):

The problem is not with the particular solution. Maple can find that

DEtools:-particularsol(ode,y(x))

And it can solve the homogeneous ODE for any A:

restart;
ode:=(1+y(x))*diff(y(x),x$2)-A*diff(y(x),x)^2=0;
A:=1;
dsolve(ode):
A:=2;
dsolve(ode):
A:=3;
dsolve(ode);

 

Is this a known issue and why it happens on some values?

Maple 2020.1 and Physics 861 on windows 10

 

 
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