44.1.24 problem 2(j)

Internal problem ID [9082]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(j)
Date solved : Tuesday, September 30, 2025 at 06:03:50 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = -\ln \left (x -1\right )+2 \ln \left (x -2\right )+c_1 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \int _1^x\frac {K[1]}{K[1]^2-3 K[1]+2}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 15

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

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