87.5.12 problem 12

Internal problem ID [23305]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:30:22 PM
CAS classification : [_exact]

\begin{align*} 2 x -y \sin \left (y x \right )+\left (6 y^{2}-x \sin \left (y x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 29

ode:=2*x-y(x)*sin(x*y(x))+(6*y(x)^2-x*sin(x*y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (x^{5}+\cos \left (\textit {\_Z} \right ) x^{3}+c_1 \,x^{3}+2 \textit {\_Z}^{3}\right )}{x} \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 25

ode=(2*x-y[x]*Sin[x*y[x]])+(6*y[x]^2-x*Sin[x*y[x]] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-x^2-2 y(x)^3-\cos (x y(x))=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (-x*sin(x*y(x)) + 6*y(x)**2)*Derivative(y(x), x) - y(x)*sin(x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out