74.15.62 problem 64 (b)

Internal problem ID [16501]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 64 (b)
Date solved : Tuesday, January 28, 2025 at 09:09:51 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(x^4*diff(y(x),x$4)+5*x^3*diff(y(x),x$3)-12*x^2*diff(y(x),x$2)-12*x*diff(y(x),x)+48*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_4 \,x^{7}+c_{2} x^{5}+x c_{3} +c_{1}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 28

DSolve[x^4*D[y[x],{x,4}]+5*x^3*D[y[x],{x,3}]-12*x^2*D[y[x],{x,2}]-12*x*D[y[x],x]+48*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_4 x^7+c_3 x^5+c_2 x+c_1}{x^3} \]