64.4.4 problem 4

Internal problem ID [13293]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 05:16:13 AM
CAS classification : [_separable]

\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

dsolve(csc(y(x))+sec(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arccos \left (\sin \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 33

DSolve[Csc[y[x]]+Sec[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sin (K[1])dK[1]\&\right ]\left [\int _1^x-\cos (K[2])dK[2]+c_1\right ] \]