87.5.18 problem 25

Internal problem ID [23311]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 25
Date solved : Thursday, October 02, 2025 at 09:31:32 PM
CAS classification : [_linear]

\begin{align*} x^{2}-2 y+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=x^2-2*y(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 16

ode=(x^2-2*y[x])+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 10

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

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