38.2.48 problem 48

Internal problem ID [6477]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 48
Date solved : Monday, January 27, 2025 at 02:07:18 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 8

dsolve([diff(y(x),x)+y(x)*cot(x)=cos(x),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 11

DSolve[{D[y[x],x]+y[x]*Cot[x]==Cos[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)}{2} \]