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Question: how to help dsolve find this ode solutions?

Question:how to help dsolve find this ode solutions?

nm 11023 Maple 2024
ode dsolve differential-equations odetest
March 12 2025
1

This is problem from INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014 ,  Chapter 2. First Order Equations. Exercises 2.4, page 57, problem 39

Maple 2024.2 can't solve it. But solution is arctan(t)-t*y(t)^2 = 0 which Maple verifies correct

> 

restart;
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1848 and is the same as the version installed in this computer, created 2025, March 11, 16:9 hours Pacific Time.`

> 

restart;
> 

ode:=(1/(1+t^2)-y(t)^2)-(2*t*y(t))*diff(y(t),t)=0;
IC:=y(0)=0;

1/(t^2+1)-y(t)^2-2*t*y(t)*(diff(y(t), t)) = 0

y(0) = 0

> 

sol:=dsolve([ode,IC])

> 

mysol:=arctan(t)-t*y(t)^2 = 0;

arctan(t)-y(t)^2*t = 0

> 

odetest(mysol,[ode,IC])

[0, 0]

 

 

Download can_not_dsolve_march_12_2025.mw

Any one has suggestion how to help dsolve find this solution?
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