89.3.7 problem 7

Internal problem ID [24305]
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 34
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:12:47 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 50

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

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

✓ Mathematica. Time used: 0.351 (sec). Leaf size: 32

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

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

✗ Sympy

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

Timed Out