Internal problem ID [5798]
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]]
\[ \boxed {y^{\prime }-y^{2}=-\frac {2}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 24
dsolve(diff(y(x),x)=y(x)^2-2/x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x^{3}+c_{1}}{\left (-x^{3}+c_{1} \right ) x} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 32
DSolve[y'[x]==y[x]^2-2/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 x^3+c_1}{x \left (x^3+c_1\right )} y(x)\to \frac {1}{x} \end{align*}