23.1.285 problem 279

Internal problem ID [4892]
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 : 279
Date solved : Sunday, October 12, 2025 at 01:18:26 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 17

ode:=x^2*diff(y(x),x) = sec(y(x))+3*x*tan(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {c_1 \,x^{4}-1}{4 x}\right ) \]

✓ Mathematica. Time used: 8.002 (sec). Leaf size: 23

ode=x^2*D[y[x],x]==Sec[y[x]]+3*x*Tan[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\arcsin \left (\frac {1}{4 x}+3 c_1 x^3\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) - 3*x*tan(y(x)) - 1/cos(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (3*x*tan(y(x)) + 1/cos(y(x)))/x**2 cannot be solved by the factorable group method