Internal problem ID [1451]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
III. Exercises 7.7. Page 389
Problem number: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
Order:=6; dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(5+11*x^2)*diff(y(x),x)+24*x^2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-2 x^{2}+3 x^{4}+\mathrm {O}\left (x^{6}\right )\right ) c_{1}+\frac {c_{2} \left (-144+432 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{4}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 27
AsymptoticDSolveValue[x^2*(1+x^2)*y''[x]+x*(5+11*x^2)*y'[x]+24*x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^4}-1\right )+c_2 \left (3 x^4-2 x^2+1\right ) \]