68.6.38 problem 39

Internal problem ID [17348]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 39
Date solved : Saturday, October 04, 2025 at 05:34:08 PM
CAS classification : [_exact, _rational, _Bernoulli]

\begin{align*} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✗ Maple

ode:=1/(t^2+1)-y(t)^2-2*t*y(t)*diff(y(t),t) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1/(1+t^2)-y[t]^2)-(2*t*y[t])*D[y[t],t]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t*y(t)*Derivative(y(t), t) - y(t)**2 + 1/(t**2 + 1),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)