23.1.40 problem 35

Internal problem ID [4647]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 35
Date solved : Tuesday, September 30, 2025 at 07:38:03 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\csc \left (x \right )+3 y \tan \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(y(x),x) = csc(x)+3*y(x)*tan(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\frac {\cos \left (x \right )^{2}}{2}+\ln \left (\sin \left (x \right )\right )+c_1 \right ) \sec \left (x \right )^{3} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 24

ode=D[y[x],x]==Csc[x]+3*y[x]*Tan[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sec ^3(x) \left (-\frac {1}{2} \sin ^2(x)+\log (\sin (x))+c_1\right ) \end{align*}

✓ Sympy. Time used: 2.120 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x)*tan(x) + Derivative(y(x), x) - 1/sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {\log {\left (- \sin ^{2}{\left (x \right )} \right )}}{2} - \frac {\sin ^{2}{\left (x \right )}}{2}}{\cos ^{3}{\left (x \right )}} \]