50.8.1 problem 1(a)

Internal problem ID [7917]
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. Problems for Review and Discovery. Page 53
Problem number : 1(a)
Date solved : Sunday, March 30, 2025 at 12:37:12 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=x*diff(y(x),x)+y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{2}+\frac {c_1}{x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 17

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

\[ y(x)\to \frac {x}{2}+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.162 (sec). Leaf size: 8

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

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