85.11.2 problem 3 (b)

Internal problem ID [22494]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 37
Problem number : 3 (b)
Date solved : Thursday, October 02, 2025 at 08:42:11 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=x^2+y(x)*sin(x*y(x))+x*sin(x*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\arccos \left (\frac {x^{3}}{3}+c_1 \right )}{x} \]

✓ Mathematica. Time used: 0.396 (sec). Leaf size: 44

ode=x^2+y[x]*Sin[x*y[x]]+ (x*Sin[x*y[x]])*D[y[x],x]== 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

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