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]]
\[ \boxed {y^{\prime \prime }-y t^{3}=0} \] With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
Order:=6; dsolve(diff(y(t),t$2)-t^3*y(t)=0,y(t),type='series',t=0);
\[ y \left (t \right ) = \left (1+\frac {t^{5}}{20}\right ) y \left (0\right )+t D\left (y \right )\left (0\right )+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 20
AsymptoticDSolveValue[y''[t]-t^3*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (\frac {t^5}{20}+1\right )+c_2 t \]