26.3.10 problem Exact Differential equations. Exercise 9.13, page 79

Internal problem ID [6943]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.13, page 79
Date solved : Tuesday, September 30, 2025 at 04:07:06 PM
CAS classification : [_exact]

\begin{align*} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 642

ode:=4*x^3-sin(x)+y(x)^3-(y(x)^2+1-3*x*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 65

ode=(4*x^3-Sin[x]+y[x]^3)-(y[x]^2+1-3*x*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left ((3 x-1) K[2]^2-\int _1^x3 K[2]^2dK[1]-1\right )dK[2]+\int _1^x\left (4 K[1]^3+y(x)^3-\sin (K[1])\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3 - (-3*x*y(x)**2 + y(x)**2 + 1)*Derivative(y(x), x) + y(x)**3 - sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out