68.1.27 problem 34

Internal problem ID [17094]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 34
Date solved : Thursday, October 02, 2025 at 01:43:10 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

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

\[ y = \frac {1}{12} x^{12}-x^{10}+\frac {9}{2} x^{8}-9 x^{6}+\frac {27}{4} x^{4}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {x^{12}}{12}-x^{10}+\frac {9 x^8}{2}-9 x^6+\frac {27 x^4}{4}+c_1 \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} + \frac {x^{12}}{12} - x^{10} + \frac {9 x^{8}}{2} - 9 x^{6} + \frac {27 x^{4}}{4} \]