89.5.3 problem 3

Internal problem ID [24353]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:21:37 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x) = csc(x)-y(x)*cot(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +c_1 \right ) \csc \left (x \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to (x+c_1) \csc (x) \end{align*}

✓ Sympy. Time used: 0.333 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {C_{1} + x}{\sin {\left (x \right )}} \]