12.2 problem 2

Internal problem ID [1766]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 2.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-y t=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*y(t)=0,y(t),type='series',t=0);
 

\[ y \relax (t ) = \left (1+\frac {t^{3}}{6}\right ) y \relax (0)+\left (t +\frac {1}{12} t^{4}\right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]

Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 28

AsymptoticDSolveValue[y''[t]-t*y[t]==0,y[t],{t,0,5}]
 

\[ y(t)\to c_2 \left (\frac {t^4}{12}+t\right )+c_1 \left (\frac {t^3}{6}+1\right ) \]