74.15.15 problem 15

Internal problem ID [16454]
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 : 15
Date solved : Tuesday, January 28, 2025 at 09:08:20 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

\[ y = \frac {c_{1} x^{4}+c_{3} x^{3}+c_{2}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 22

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

\[ y(x)\to c_3 x^2+\frac {c_1}{x^2}+c_2 x \]