Internal problem ID [1776]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 12(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} 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: 24
Order:=6; dsolve(diff(y(t),t$2)+t^3*diff(y(t),t)+3*t^2*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1-\frac {t^{4}}{4}\right ) y \relax (0)+\left (t -\frac {1}{5} t^{5}\right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[t]+t^3*y'[t]+3*t^2*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_2 \left (t-\frac {t^5}{5}\right )+c_1 \left (1-\frac {t^4}{4}\right ) \]