Internal problem ID [10873]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left (y+1\right )^{2}-\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x*(y(x)+1)^2=(x^2+1)*y(x)*exp(y(x))*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1}}{\frac {\ln \left (x^{2}+1\right )}{2}+c_{1}}\right )-1 \]
✓ Solution by Mathematica
Time used: 0.639 (sec). Leaf size: 33
DSolve[x*(y[x]+1)^2==(x^2+1)*y[x]*Exp[y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-W\left (-\frac {2}{e \log \left (x^2+1\right )+2 e c_1}\right ) \\ y(x)\to -1 \\ \end{align*}