89.3.10 problem 10

Internal problem ID [24308]
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 : 10
Date solved : Thursday, October 02, 2025 at 10:12:57 PM
CAS classification : [_exact, _rational]

\begin{align*} w^{3}+w z^{2}-z+\left (z^{3}+w^{2} z-w \right ) z^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=w^3+w*z(w)^2-z(w)+(z(w)^3+w^2*z(w)-w)*diff(z(w),w) = 0; 
dsolve(ode,z(w), singsol=all);
 

\[ \frac {w^{4}}{4}+\frac {w^{2} z^{2}}{2}-w z+\frac {z^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.138 (sec). Leaf size: 1807

ode=( w^3+w*z[w]^2-z[w]  )+( z[w]^3+w^2*z[w] -w  )*D[z[w],w]==0; 
ic={}; 
DSolve[{ode,ic},z[w],w,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

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

Timed Out