32.2.47 problem 48

Internal problem ID [7764]
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 : Tuesday, September 30, 2025 at 05:05:10 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*}

✓ Maple. Time used: 0.117 (sec). Leaf size: 8

ode:=diff(y(x),x)+y(x)*cot(x) = cos(x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to \frac {\sin (x)}{2} \end{align*}

✓ Sympy. Time used: 0.692 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {\frac {1}{2} - \frac {\cos ^{2}{\left (x \right )}}{2}}{\sin {\left (x \right )}} \]