Internal problem ID [5282]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number: 1(e).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x +c_{3} x \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[x^3*y'''[x]+2*x^2*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x}+c_2 x+c_3 x \log (x) \\ \end{align*}