23.1.38 problem 33

Internal problem ID [4645]
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 : 33
Date solved : Tuesday, September 30, 2025 at 07:37:59 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\sin \left (x \right )+2 y \tan \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(x),x) = sin(x)+2*y(x)*tan(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 19

ode=D[y[x],x]==Sin[x]+2*y[x]*Tan[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\cos (x)}{3}+c_1 \sec ^2(x) \end{align*}

✓ Sympy. Time used: 0.881 (sec). Leaf size: 14

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

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