47.2.46 problem 42

Internal problem ID [7462]
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
Date solved : Monday, January 27, 2025 at 03:01:07 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} \left (y^{\prime }-x \right )&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(x^3*(diff(y(x),x)-x)=y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 29

DSolve[x^3*(D[y[x],x]-x)==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2 (\log (x)-1+c_1)}{\log (x)+c_1} \\ y(x)\to x^2 \\ \end{align*}