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

Internal problem ID [6956]
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 : Tuesday, September 30, 2025 at 04:07:15 PM
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+cos(x)*y(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: 0.104 (sec). Leaf size: 52

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]
 

\[ \text {Solve}\left [-y(x) \int _1^x\cos (K[1])dK[1]+\int _1^x\left (K[1]^2+\cos (K[1]) y(x)\right )dK[1]+\frac {y(x)^4}{4}+y(x) \sin (x)=c_1,y(x)\right ] \]

✗ 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