13.12.2 problem 2

Internal problem ID [2414]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8, Series solutions. Page 195
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:52:23 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-y t&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

Order:=6; 
dsolve(diff(y(t),t$2)-t*y(t)=0,y(t),type='series',t=0);
 

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

✓ Solution by Mathematica

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

AsymptoticDSolveValue[D[y[t],{t,2}]-t*y[t]==0,y[t],{t,0,"6"-1}]
 

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