13.12.13 problem 12(b)

Internal problem ID [2425]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8, Series solutions. Page 195
Problem number : 12(b)
Date solved : Monday, January 27, 2025 at 05:52:33 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} 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 )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 4

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

\[ y(t)\to 0 \]