Internal problem ID [5289]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 4. Linear equations with Regular Singular Points. Page 154
Problem number: 1(c).
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 y^{\prime }+3 x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=8; dsolve(x^2*diff(y(x),x$2)-5*diff(y(x),x)+3*x^2*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 106
AsymptoticDSolveValue[x^2*y''[x]-5*y'[x]+3*x^2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {339 x^7}{8750}+\frac {49 x^6}{1250}+\frac {18 x^5}{625}+\frac {3 x^4}{50}+\frac {x^3}{5}+1\right )+c_2 e^{-5/x} \left (-\frac {302083 x^7}{218750}+\frac {5243 x^6}{6250}-\frac {357 x^5}{625}+\frac {113 x^4}{250}-\frac {49 x^3}{125}+\frac {6 x^2}{25}-\frac {2 x}{5}+1\right ) x^2 \]