23.1.120 problem 123

Internal problem ID [4727]
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 : 123
Date solved : Sunday, October 12, 2025 at 01:18:04 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 15

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

\[ y = \arcsin \left (\sec \left (x \right ) \left (-\ln \left (\cos \left (x \right )\right )+c_1 \right )\right ) \]

✓ Mathematica. Time used: 10.535 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \arcsin \left (\frac {1}{4} \sec (x) (-4 \log (\cos (x))+c_1)\right ) \end{align*}

✓ Sympy. Time used: 6.223 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1} + \log {\left (\cos {\left (x \right )} \right )}}{\cos {\left (x \right )}} \right )} + \pi , \ y{\left (x \right )} = - \operatorname {asin}{\left (\frac {C_{1} + \log {\left (\cos {\left (x \right )} \right )}}{\cos {\left (x \right )}} \right )}\right ] \]