19.1.13 problem 13

Internal problem ID [4225]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 07:07:45 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 8

ode:=cot(x)*diff(y(x),x) = y(x); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \sec \left (x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 9

ode=Cot[x]*D[y[x],x]==y[x]; 
ic=y[0]==2; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.143 (sec). Leaf size: 7

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

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