6.8 problem 1(h)

Internal problem ID [5479]

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]]]

Solve \begin {gather*} \boxed {y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.086 (sec). Leaf size: 27

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

\[ x -\frac {\left (y \relax (x )^{2}-2 y \relax (x )+2\right ) {\mathrm e}^{y \relax (x )}+c_{1}}{y \relax (x )^{2}} = 0 \]

Solution by Mathematica

Time used: 0.431 (sec). Leaf size: 32

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

\[ \text {Solve}\left [x=\frac {e^{y(x)} \left (y(x)^2-2 y(x)+2\right )}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]