38.4.17 problem 5 (a)

Internal problem ID [8316]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 5 (a)
Date solved : Tuesday, September 30, 2025 at 05:26:15 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 9

ode:=diff(y(x),x) = x; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=D[y[x],x]==x; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.026 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {x^{2}}{2} \]