10.6.11 problem 11

Internal problem ID [1228]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:46:02 AM
CAS classification : [_exact]

\begin{align*} x^{2}+y+\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(x^2+y(x)+(exp(y(x))+x)*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ y = \frac {-x^{3}-3 x \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {x^{3}+3 c_1}{3 x}}}{x}\right )-3 c_1}{3 x} \]

✓ Solution by Mathematica

Time used: 3.315 (sec). Leaf size: 42

DSolve[x^2+y[x]+(Exp[y[x]]+x)*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -W\left (\frac {e^{-\frac {x^2}{3}+\frac {c_1}{x}}}{x}\right )-\frac {x^2}{3}+\frac {c_1}{x} \]