Internal problem ID [6521]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime } x^{2}-9 y^{\prime } x +25 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
Order:=6; dsolve(x^2*diff(y(x), x$2)-9*x*diff(y(x), x)+25*y(x) = 0,y(x),type='series',x=0);
\[ y \left (x \right ) = x^{5} \left (c_{2} \ln \left (x \right )+c_{1} \right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
AsymptoticDSolveValue[x^2*y''[x]-9*x*y'[x]+25*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x^5+c_2 x^5 \log (x) \]