4.31 problem 34

Internal problem ID [6194]

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.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 18

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)
 

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

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {c_1}{x^4}+c_3 x^2+c_2 x \\ \end{align*}