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 : Sunday, March 30, 2025 at 12:09:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \frac {x^{2} \left (\ln \left (x \right )-c_1 -1\right )}{\ln \left (x \right )-c_1} \]

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

ode=x^3*(D[y[x],x]-x)==y[x]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.251 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(-x + Derivative(y(x), x)) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (1 - 8 x^{2}\right ) \]