38.2.15 problem 15

Internal problem ID [6444]
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 : 15
Date solved : Monday, January 27, 2025 at 02:04:17 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cot \left (x \right )&=5 \,{\mathrm e}^{\cos \left (x \right )} \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([diff(y(x),x)+y(x)*cot(x)=5*exp(cos(x)),y(1/2*Pi) = -4],y(x), singsol=all)
 

\[ y = -5 \csc \left (x \right ) {\mathrm e}^{\cos \left (x \right )}+\csc \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 16

DSolve[{D[y[x],x]+y[x]*Cot[x]==5*Exp[Cos[x]],{y[Pi/2]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (1-5 e^{\cos (x)}\right ) \csc (x) \]