Internal problem ID [6523]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 52.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 35
Order:=6; dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-(x^2+5/4)*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{3} \left (1+\frac {1}{10} x^{2}+\frac {1}{280} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (12-6 x^{2}-\frac {3}{2} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 58
AsymptoticDSolveValue[x^2*y''[x]-x*y'[x]-(x^2+5/4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^{7/2}}{8}-\frac {x^{3/2}}{2}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {x^{13/2}}{280}+\frac {x^{9/2}}{10}+x^{5/2}\right ) \]