50.3.21 problem 4(a)

Internal problem ID [7845]
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)
Date solved : Monday, January 27, 2025 at 03:25:36 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 22

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

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