87.5.20 problem 27

Internal problem ID [23313]
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 : 27
Date solved : Thursday, October 02, 2025 at 09:31:39 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=(y[x]-2*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: 0.092 (sec). Leaf size: 10

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

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