44.3.1 problem 7

Internal problem ID [6982]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 04:01:09 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 9

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

\[ y = 2 x +c_{1} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 11

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

\[ y(x)\to 2 x+c_1 \]

✓ Sympy. Time used: 0.067 (sec). Leaf size: 7

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

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