18.1.8 problem Problem 14.5 (b)

Internal problem ID [3464]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.5 (b)
Date solved : Monday, January 27, 2025 at 07:37:48 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

dsolve(diff(y(x),x)-y(x)*cot(x)+1/sin(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 13

DSolve[D[y[x],x]-y[x]*Cot[x]+1/Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x)+c_1 \sin (x) \]