13.12.12 problem 12(a)

Internal problem ID [2424]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8, Series solutions. Page 195
Problem number : 12(a)
Date solved : Monday, January 27, 2025 at 05:52:32 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*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

\[ y = \left (1-\frac {t^{4}}{4}\right ) y \left (0\right )+\left (t -\frac {1}{5} t^{5}\right ) y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(t)\to c_2 \left (t-\frac {t^5}{5}\right )+c_1 \left (1-\frac {t^4}{4}\right ) \]