3.21 problem 4(a)

Internal problem ID [5424]

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 1.4 First Order Linear Equations. Page 15
Problem number: 4(a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]

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

Solution by Maple

Time used: 0.11 (sec). Leaf size: 16

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

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

Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 22

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

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