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Question: Should not dsolve give implicit solution if unable to find explicit?

Question:Should not dsolve give implicit solution if unable to find explicit?

nm 11363 Maple 2025
ode dsolve implicit differential-equations
3 hours ago
0

THis is problem from textbook. Maple do not give solution. 

But when asked for implicit solution, it gives one.  Should it not have done this automatically?

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

ode:=y(x)*diff(y(x),x) = a;
ic:=y(0) = b;
sol:=dsolve([ode,ic]);

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

y(0) = b

> 

sol:=dsolve([ode,ic],'implicit')

-2*a*x+y(x)^2-b^2 = 0

 

 

Download why_no_solution_maple_2025_1.mw

We see now there are two solutions for y(x), since quadratic.

So why dsolve do not solve this and at least give implicit solution automatically? Should this be reported as defect?
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