Internal problem ID [2463]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.6. page
783
Problem number: 2.
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 }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-9/4)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{3} \left (1-\frac {1}{10} x^{2}+\frac {1}{280} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (12+6 x^{2}-\frac {3}{2} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 58
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(x^2-9/4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^{5/2}}{8}+\frac {1}{x^{3/2}}+\frac {\sqrt {x}}{2}\right )+c_2 \left (\frac {x^{11/2}}{280}-\frac {x^{7/2}}{10}+x^{3/2}\right ) \]