50.1.22 problem 2(h)

Internal problem ID [7794]
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 : Monday, January 27, 2025 at 03:23:19 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 13

DSolve[Sin[x]*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\text {arctanh}(\cos (x))+c_1 \]