88.7.3 problem 3

Internal problem ID [23998]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 41
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:50:28 PM
CAS classification : [_exact]

\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 25

ode:=3*y(x)^2+y(x)*sin(2*x*y(x))+(6*x*y(x)+x*sin(2*x*y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (4 c_1 x +3 \textit {\_Z}^{2}-2 x \cos \left (\textit {\_Z} \right )\right )}{2 x} \]

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 24

ode=( 3*y[x]^2+y[x]*Sin[2*x*y[x] ] )+( 6*x*y[x] + x*Sin[2*x*y[x]] )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [3 x y(x)^2-\frac {1}{2} \cos (2 x y(x))=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((6*x*y(x) + x*sin(2*x*y(x)))*Derivative(y(x), x) + 3*y(x)**2 + y(x)*sin(2*x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out