23.1.31 problem 26

Internal problem ID [4638]
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 : 26
Date solved : Tuesday, September 30, 2025 at 07:37:46 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)+tan(x) = (1-y(x))*sec(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x +c_1}{\sec \left (x \right )+\tan \left (x \right )} \]

✓ Mathematica. Time used: 0.359 (sec). Leaf size: 21

ode=D[y[x],x]+Tan[x]==(1-y[x])*Sec[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (x+c_1) e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \end{align*}

✓ Sympy. Time used: 43.027 (sec). Leaf size: 82

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

\[ y{\left (x \right )} = \frac {\left (C_{1} + \int \frac {\sqrt {\sin {\left (x \right )} + 1} \left (y{\left (x \right )} + \sin {\left (x \right )} - 1\right )}{\sqrt {\sin {\left (x \right )} - 1} \cos {\left (x \right )}}\, dx\right ) \sqrt {\sin {\left (x \right )} - 1}}{\sqrt {\sin {\left (x \right )} - 1} \int \frac {\sqrt {\sin {\left (x \right )} + 1}}{\sqrt {\sin {\left (x \right )} - 1} \cos {\left (x \right )}}\, dx - \sqrt {\sin {\left (x \right )} + 1}} \]