3.22 problem 4(b)

Internal problem ID [5425]

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(b).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]

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

Solution by Maple

Time used: 0.141 (sec). Leaf size: 14

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

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

Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 18

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

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