32.4.10 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.2, page 90

Internal problem ID [5821]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.2, page 90
Date solved : Sunday, March 30, 2025 at 10:18:47 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

\[ \frac {x^{3}}{3}+\sin \left (x \right ) y+\frac {y^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.196 (sec). Leaf size: 1119

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out