7.7.3 problem 3

Internal problem ID [181]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 3
Date solved : Friday, February 07, 2025 at 08:01:34 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x y+y^{2}-y^{\prime } x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(x*y(x)+y(x)^2-x^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{-\ln \left (x \right )+c_1} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 21

DSolve[x*y[x]+y[x]^2-x^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{-\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}