Internal problem ID [5045]
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: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+\frac {2}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.781 (sec). Leaf size: 24
dsolve(diff(y(x),x)=y(x)^2-2/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x^{3}+c_{1}}{x \left (-x^{3}+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 29
DSolve[y'[x]==y[x]^2-2/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x}-\frac {3 x^2}{x^3+c_1} \\ y(x)\to \frac {1}{x} \\ \end{align*}