7.5.9 problem 9

Internal problem ID [113]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 9
Date solved : Friday, February 07, 2025 at 07:50:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 21

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

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