89.4.16 problem 17

Internal problem ID [24338]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:19:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.085 (sec). Leaf size: 26

ode:=x^4*diff(y(x),x) = -x^3*y(x)-csc(x*y(x)); 
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: 4.168 (sec). Leaf size: 40

ode=x^4*D[y[x],x]==-x^3*y[x]-Csc[x*y[x]]; 
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) + csc(x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out