13.12.3 problem 3

Internal problem ID [2415]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8, Series solutions. Page 195
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:52:23 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

\[ y = \left (1+\frac {3}{4} t^{2}+\frac {3}{32} t^{4}\right ) y \left (0\right )+\left (\frac {1}{3} t^{3}+t \right ) y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 35

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

\[ y(t)\to c_2 \left (\frac {t^3}{3}+t\right )+c_1 \left (\frac {3 t^4}{32}+\frac {3 t^2}{4}+1\right ) \]