Internal problem ID [1794]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(t = 2\).
✗ Solution by Maple
Order:=6; dsolve(t*(t-2)^2*diff(y(t),t$2)+t*diff(y(t),t)+y(t)=0,y(t),type='series',t=2);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 112
AsymptoticDSolveValue[t*(t-2)^2*y''[t]+t*y'[t]+y[t]==0,y[t],{t,2,5}]
\[ y(t)\to c_2 e^{\frac {1}{t-2}} \left (\frac {247853}{240} (t-2)^5+\frac {4069}{24} (t-2)^4+\frac {199}{6} (t-2)^3+8 (t-2)^2+\frac {5 (t-2)}{2}+1\right ) (t-2)^2+c_1 \left (-\frac {641}{480} (t-2)^5+\frac {25}{48} (t-2)^4-\frac {7}{24} (t-2)^3+\frac {1}{4} (t-2)^2+\frac {2-t}{2}+1\right ) \]