14.15.5 problem 5

Internal problem ID [2670]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.3, Equal roots and roots differing by an integer. Excercises page 223
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:05:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.143 (sec). Leaf size: 8537

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

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 11270

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

Too large to display