Internal problem ID [2565]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve(diff(y(x),x)=exp(x)*(y(x)^2+1),y(x), singsol=all)
\[ y \relax (x ) = \tan \left ({\mathrm e}^{x}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.3 (sec). Leaf size: 26
DSolve[y'[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*}