Internal problem ID [2640]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(x*(y(x)^2+1)+(2*y(x)+1)*exp(-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (x \,{\mathrm e}^{x}-{\mathrm e}^{x}+\ln \left (\frac {2}{\cos \left (2 \textit {\_Z} \right )+1}\right )+\textit {\_Z} +c_{1}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.624 (sec). Leaf size: 43
DSolve[x*(y[x]^2+1)+(2*y[x]+1)*Exp[-x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\log \left (\text {$\#$1}^2+1\right )+\text {ArcTan}(\text {$\#$1})\&\right ]\left [-e^x (x-1)+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}