23.1.389 problem 374

Internal problem ID [4996]
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 : 374
Date solved : Tuesday, September 30, 2025 at 09:13:25 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right )&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 26

ode:=x^4*diff(y(x),x)+x^3*y(x)+csc(x*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {\pi }{2}+\arcsin \left (\frac {2 c_1 \,x^{2}+1}{2 x^{2}}\right )}{x} \]

✓ Mathematica. Time used: 4.503 (sec). Leaf size: 40

ode=x^4*D[y[x],x]+x^3*y[x]+Csc[x*y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\arccos \left (-\frac {1}{2 x^2}+c_1\right )}{x}\\ y(x)&\to \frac {\arccos \left (-\frac {1}{2 x^2}+c_1\right )}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), x) + x**3*y(x) + 1/sin(x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) + y(x)/x + 1/(x**4*sin(x*y(x))) cannot be solved by the factorable group method