67.1.10 problem Problem 2(a)

Internal problem ID [13957]
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)
Date solved : Tuesday, January 28, 2025 at 06:09:40 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = -\operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-1}}{\ln \left (x^{2}+1\right )+2 c_{1}}\right )-1 \]

✓ Solution by Mathematica

Time used: 0.664 (sec). Leaf size: 33

DSolve[x*(y[x]+1)^2==(x^2+1)*y[x]*Exp[y[x]]*D[y[x],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*}