14.5.3 problem 3

Internal problem ID [2540]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.17. What to do in practice. Excercises page 126
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:09:33 AM
CAS classification : [_rational]

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

With initial conditions

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]==(t^2+y[t]^2)/(1+t+y[t]^2); 
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((-t**2 - y(t)**2)/(t + y(t)**2 + 1) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out