Internal problem ID [5041]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{3} \left (y^{\prime }-x \right )-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(x^3*(diff(y(x),x)-x)=y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (\ln \relax (x )-c_{1}-1\right )}{\ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 27
DSolve[x^3*(y'[x]-x)==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (1-\frac {1}{\log (x)+c_1}\right ) \\ y(x)\to x^2 \\ \end{align*}