Internal problem ID [2410]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x^{2}+\left (x^{2}-2\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)+(x^2-2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{2} \left (1+\frac {1}{2} x +\frac {1}{20} x^{2}-\frac {1}{60} x^{3}-\frac {1}{210} x^{4}-\frac {1}{3360} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12+6 x +6 x^{2}+5 x^{3}+x^{4}-\frac {1}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 68
AsymptoticDSolveValue[x^2*y''[x]-x^2*y'[x]+(x^2-2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{12}+\frac {5 x^2}{12}+\frac {x}{2}+\frac {1}{x}+\frac {1}{2}\right )+c_2 \left (-\frac {x^6}{210}-\frac {x^5}{60}+\frac {x^4}{20}+\frac {x^3}{2}+x^2\right ) \]