44.1.51 problem 63 (a)

Internal problem ID [6926]
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. Exercises 1.1 at page 12
Problem number : 63 (a)
Date solved : Sunday, March 30, 2025 at 11:29:17 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=f \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \int f \left (x \right )d x +c_1 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

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

\[ y(x)\to \int _1^xf(K[1])dK[1]+c_1 \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} + \int f{\left (x \right )}\, dx \]