Internal problem ID [1767]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
Order:=6; dsolve((2+t^2)*diff(y(t),t$2)-t*diff(y(t),t)-3*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1+\frac {3}{4} t^{2}+\frac {3}{32} t^{4}\right ) y \relax (0)+\left (\frac {1}{3} t^{3}+t \right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[(2+t^2)*y''[t]-t*y'[t]-3*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_2 \left (\frac {t^3}{3}+t\right )+c_1 \left (\frac {3 t^4}{32}+\frac {3 t^2}{4}+1\right ) \]