Internal problem ID [5478]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page
32
Problem number: 1(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 27
dsolve(y(x)+(2*x-y(x)*exp(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ x -\frac {\left (y \left (x \right )^{2}-2 y \left (x \right )+2\right ) {\mathrm e}^{y \left (x \right )}+c_{1}}{y \left (x \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.219 (sec). Leaf size: 32
DSolve[y[x]+(2*x-y[x]*Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {e^{y(x)} \left (y(x)^2-2 y(x)+2\right )}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]