50.4.2 problem 2

Internal problem ID [7851]
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 1.5. Exact Equations. Page 20
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:25:49 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \end{align*}

✗ Solution by Maple

dsolve((sin(x)*tan(y(x))+1)+(cos(x)*sec(y(x))^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 1.944 (sec). Leaf size: 54

DSolve[(Sin[x]*Tan[y[x]]+1)+(Cos[x]*Sec[y[x]]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arctan (\sin (x)+c_1 \cos (x)) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ y(x)\to \frac {1}{2} \pi \sqrt {\cos ^2(x)} \sec (x) \\ \end{align*}