14.12.7 problem 7

Internal problem ID [2617]
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 : 7
Date solved : Monday, January 27, 2025 at 06:04:39 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*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

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

\[ y = \left (-2\right ) t +\operatorname {O}\left (t^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(t)\to -2 t \]