Internal problem ID [1799]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(2*t^2*diff(y(t),t$2)+3*t*diff(y(t),t)-(1+t)*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \frac {c_{2} t^{\frac {3}{2}} \left (1+\frac {1}{5} t +\frac {1}{70} t^{2}+\frac {1}{1890} t^{3}+\frac {1}{83160} t^{4}+\frac {1}{5405400} t^{5}+\mathrm {O}\left (t^{6}\right )\right )+c_{1} \left (1-t -\frac {1}{2} t^{2}-\frac {1}{18} t^{3}-\frac {1}{360} t^{4}-\frac {1}{12600} t^{5}+\mathrm {O}\left (t^{6}\right )\right )}{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 86
AsymptoticDSolveValue[2*t^2*y''[t]+3*t*y'[t]-(1+t)*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \sqrt {t} \left (\frac {t^5}{5405400}+\frac {t^4}{83160}+\frac {t^3}{1890}+\frac {t^2}{70}+\frac {t}{5}+1\right )+\frac {c_2 \left (-\frac {t^5}{12600}-\frac {t^4}{360}-\frac {t^3}{18}-\frac {t^2}{2}-t+1\right )}{t} \]