44.3.16 problem 2(f)

Internal problem ID [9126]
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 1.4 First Order Linear Equations. Page 15
Problem number : 2(f)
Date solved : Tuesday, September 30, 2025 at 06:04:45 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 13

ode:=x^2*diff(y(x),x)+x*y(x) = 2*x; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 x -1}{x} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 12

ode=x^2*D[y[x],x]+x*y[x]==2*x; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2-\frac {1}{x} \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + x*y(x) - 2*x,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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