Internal problem ID [5281]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x^{3}+x^{3} \ln \relax (x ) c_{1}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 22
DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (c_1 x+3 c_2 x \log (x)+1) \\ \end{align*}