81.2.8 problem 3-9

Internal problem ID [21497]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 3. Exact differential equations. Page 42.
Problem number : 3-9
Date solved : Thursday, October 02, 2025 at 07:42:09 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: 0.057 (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)
 

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