74.1.27 problem 34

Internal problem ID [15807]
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 : Tuesday, January 28, 2025 at 08:07:58 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 39

DSolve[D[y[x],x]==(x^2-1)*(x^3-3*x)^3,y[x],x,IncludeSingularSolutions -> True]
 

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