Internal problem ID [4397]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page
564
Problem number: 7, using elementary method.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{1}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[x^2*y''[x]-3*x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 x^2+c_1\right ) \\ \end{align*}