14.4.14 problem 14

Internal problem ID [2532]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 14
Date solved : Monday, January 27, 2025 at 05:59:18 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \end{align*}

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(t),t)=exp(-t)+ln(1+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]==Exp[-t]+Log[1+y[t]^2],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

Not solved