65.3.2 problem 1 (B)

Internal problem ID [15639]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 1 (B)
Date solved : Thursday, October 02, 2025 at 10:21:34 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x -1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x) = x-1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{2} x^{2}-x +c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.061 (sec). Leaf size: 10

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

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