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 : Monday, January 27, 2025 at 05:59:45 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*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved