Internal problem ID [3149]
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]
\[ \boxed {x \left (y^{2}+1\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left ({\mathrm e}^{x} x +\ln \left (\frac {2}{1+\cos \left (2 \textit {\_Z} \right )}\right )+\textit {\_Z} -{\mathrm e}^{x}+c_{1} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.627 (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 {$\#$1}^2+1\right )+\arctan (\text {$\#$1})\&\right ]\left [-e^x (x-1)+c_1\right ] y(x)\to -i y(x)\to i \end{align*}