44.1.22 problem 2(h)

Internal problem ID [9080]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(h)
Date solved : Tuesday, September 30, 2025 at 06:03:48 PM
CAS classification : [_quadrature]

\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \end{align*}

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

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

\[ y = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.109 (sec). Leaf size: 20

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

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