Internal problem ID [1810]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 40
Order:=6; dsolve(t*diff(y(t),t$2)-(4+t)*diff(y(t),t)+2*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = c_{1} t^{5} \left (1+\frac {1}{2} t +\frac {1}{7} t^{2}+\frac {5}{168} t^{3}+\frac {5}{1008} t^{4}+\frac {1}{1440} t^{5}+\mathrm {O}\left (t^{6}\right )\right )+c_{2} \left (2880+1440 t +240 t^{2}+4 t^{5}+\mathrm {O}\left (t^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 56
AsymptoticDSolveValue[t*y''[t]-(4+t)*y'[t]+2*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (\frac {t^2}{12}+\frac {t}{2}+1\right )+c_2 \left (\frac {5 t^9}{1008}+\frac {5 t^8}{168}+\frac {t^7}{7}+\frac {t^6}{2}+t^5\right ) \]