50.3.22 problem 4(b)

Internal problem ID [7846]
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)
Date solved : Monday, January 27, 2025 at 03:25:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y-x y^{\prime }&=y^{\prime } y^{2} {\mathrm e}^{y} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 17

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

\[ -y \,{\mathrm e}^{y}-c_{1} y+x = 0 \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 18

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

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