Internal problem ID [11919]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.2 (Frobenius).
Exercises page 251
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
Order:=6; dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+3/4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \sqrt {x}\, \left (c_{1} x +c_{2} \right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
AsymptoticDSolveValue[x^2*y''[x]-x*y'[x]+3/4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x^{3/2}+c_1 \sqrt {x} \]