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(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y-y^{\prime } x -y^{\prime } y^{2} {\mathrm e}^{y}=0} \]
✓ Solution by Maple
Time used: 0.032 (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)
\[ x -\left ({\mathrm e}^{y \left (x \right )}+c_{1} \right ) y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 18
DSolve[y[x]-x*y'[x]==y'[x]*y[x]^2*Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]