7.8 problem 8

Internal problem ID [2018]

Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section: Exercise 11, page 45
Problem number: 8.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]

\[ \boxed {y^{\prime } x^{2}+y^{2}-y x=0} \]

Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

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

\[ y \left (x \right ) = \frac {x}{\ln \left (x \right )+c_{1}} \]

Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 19

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

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