Internal problem ID [1768]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-t^{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: 19
Order:=6; dsolve(diff(y(t),t$2)-t^3*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1+\frac {t^{5}}{20}\right ) y \relax (0)+t D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 20
AsymptoticDSolveValue[y''[t]-t^3*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (\frac {t^5}{20}+1\right )+c_2 t \]