44.1.1 problem 1(a)

Internal problem ID [9059]
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 : 1(a)
Date solved : Tuesday, September 30, 2025 at 06:03:17 PM
CAS classification : [_quadrature]

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

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

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

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

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

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

\begin{align*} y(x)&\to x^2+c_1 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 7

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

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