Internal problem ID [1805]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.2, Regular singular points, the method of Frobenius. Page 214
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✗ Solution by Maple
Order:=6; dsolve(t^3*diff(y(t),t$2)-t*diff(y(t),t)-(t^2+5/4)*y(t)=0,y(t),type='series',t=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 97
AsymptoticDSolveValue[t^3*y''[t]-t*y'[t]-(t^2+5/4)*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_2 e^{-1/t} \left (-\frac {239684276027 t^5}{8388608}+\frac {1648577803 t^4}{524288}-\frac {3127415 t^3}{8192}+\frac {26113 t^2}{512}-\frac {117 t}{16}+1\right ) t^{13/4}+\frac {c_1 \left (-\frac {784957 t^5}{8388608}-\frac {152693 t^4}{524288}-\frac {7649 t^3}{8192}-\frac {31 t^2}{512}+\frac {45 t}{16}+1\right )}{t^{5/4}} \]