23.1.136 problem 140

Internal problem ID [4743]
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 : 140
Date solved : Tuesday, September 30, 2025 at 08:20:54 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

ode:=diff(y(x),x) = sec(x)^2+y(x)*sec(x)*Csx(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int \sec \left (x \right )^{2} {\mathrm e}^{-\int \sec \left (x \right ) \operatorname {Csx} \left (x \right )d x}d x +c_1 \right ) {\mathrm e}^{\int \sec \left (x \right ) \operatorname {Csx} \left (x \right )d x} \]

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to \exp \left (\int _1^x\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \sec ^2(K[2])dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 17.681 (sec). Leaf size: 85

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-Csx(x)*y(x)/cos(x) + Derivative(y(x), x) - 1/cos(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\left (C_{1} + \int \frac {e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos ^{2}{\left (x \right )}}\, dx + \int \frac {\operatorname {Csx}{\left (x \right )} y{\left (x \right )} e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos {\left (x \right )}}\, dx\right ) e^{\int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\left (e^{\int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}\right ) \int \frac {\operatorname {Csx}{\left (x \right )} e^{- \int \frac {\operatorname {Csx}{\left (x \right )}}{\cos {\left (x \right )}}\, dx}}{\cos {\left (x \right )}}\, dx + 1} \]