32.2.15 problem 15

Internal problem ID [7732]
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 : Tuesday, September 30, 2025 at 05:02:47 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*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to \left (1-5 e^{\cos (x)}\right ) \csc (x) \end{align*}

✓ Sympy. Time used: 0.691 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)/tan(x) - 5*exp(cos(x)) + Derivative(y(x), x),0) 
ics = {y(pi/2): -4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1 - 5 e^{\cos {\left (x \right )}}}{\sin {\left (x \right )}} \]