Internal problem ID [87]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x) = x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{\ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 21
DSolve[x^2*y'[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*}