64.8.10 problem 13

Internal problem ID [13398]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 05:41:45 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(x^3*diff(y(x),x$3)-4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{3} x^{3}+c_{1} x +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 20

DSolve[x^3*D[y[x],{x,3}]-4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_3 x^3+c_2 x+c_1\right ) \]