25.1.23 problem 23

Internal problem ID [4235]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 23
Date solved : Monday, January 27, 2025 at 08:43:23 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 9

dsolve(diff(y(x),x)=exp(x)*(y(x)^2+1),y(x), singsol=all)
 

\[ y \left (x \right ) = \tan \left ({\mathrm e}^{x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.324 (sec). Leaf size: 26

DSolve[D[y[x],x]==Exp[x]*(y[x]^2+1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \tan \left (e^x+c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}