29.10.10 problem 276

Internal problem ID [4876]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 276
Date solved : Sunday, March 30, 2025 at 04:08:28 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: 9.362 (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]
 

\[ y(x)\to -\arcsin \left (\frac {1}{4 x}+3 c_1 x^3\right ) \]

✗ 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