14.1.25 problem Problem 33

Internal problem ID [3582]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 33
Date solved : Tuesday, September 30, 2025 at 06:47:46 AM
CAS classification : [_quadrature]

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

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

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

\[ y = -\cos \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.024 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} - \cos {\left (x \right )} \]