47.2.50 problem 46

Internal problem ID [7466]
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
Date solved : Monday, January 27, 2025 at 03:01:11 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Riccati, _special]]

\begin{align*} y^{\prime }&=y^{2}-\frac {2}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.726 (sec). Leaf size: 24

dsolve(diff(y(x),x)=y(x)^2-2/x^2,y(x), singsol=all)
 

\[ y = \frac {2 x^{3}+c_{1}}{x \left (-x^{3}+c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 32

DSolve[D[y[x],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*}