Internal problem ID [5373]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (x )-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(sin(x)*diff(y(x),x)=1,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\csc \relax (x )-\cot \relax (x )\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 24
DSolve[Sin[x]*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1 \\ \end{align*}