64.3.17 problem 22

Internal problem ID [13288]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 05:16:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {x^2}{x-c_1} \\ y(x)\to 0 \\ \end{align*}