Internal problem ID [578]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(x^2+y(x)+(exp(y(x))+x)*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (\frac {{\mathrm e}^{-\frac {x^{2}}{3}} {\mathrm e}^{-\frac {c_{1}}{x}}}{x}\right )-\frac {x^{3}+3 c_{1}}{3 x} \]
✓ Solution by Mathematica
Time used: 3.52 (sec). Leaf size: 42
DSolve[x^2+y[x]+(Exp[y[x]]+x)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ProductLog}\left (\frac {e^{-\frac {x^2}{3}+\frac {c_1}{x}}}{x}\right )-\frac {x^2}{3}+\frac {c_1}{x} \\ \end{align*}