54.4.31 problem 34

Internal problem ID [8615]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots Nonintegral. Exercises page 365
Problem number : 34
Date solved : Monday, January 27, 2025 at 04:17:31 PM
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: 0.004 (sec). Leaf size: 20

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)
 

\[ y = \frac {c_{2} x^{6}+c_3 \,x^{5}+c_{1}}{x^{4}} \]

✓ Solution by Mathematica

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

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]
 

\[ y(x)\to \frac {c_1}{x^4}+c_3 x^2+c_2 x \]