14.12.4 problem 4

Internal problem ID [2614]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8. Series solutions. Excercises page 197
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:04:36 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-t^{3} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

Order:=6; 
dsolve(diff(y(t),t$2)-t^3*y(t)=0,y(t),type='series',t=0);
 

\[ y = \left (1+\frac {t^{5}}{20}\right ) y \left (0\right )+t y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 20

AsymptoticDSolveValue[D[y[t],{t,2}]-t^3*y[t]==0,y[t],{t,0,"6"-1}]
 

\[ y(t)\to c_1 \left (\frac {t^5}{20}+1\right )+c_2 t \]