7.14.5 problem 5

Internal problem ID [430]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:53:35 AM
CAS classification : [[_2nd_order, _missing_y]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

Order:=6; 
dsolve((x^2-3)*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+\left (x +\frac {1}{9} x^{3}+\frac {1}{45} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 25

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

\[ y(x)\to c_2 \left (\frac {x^5}{45}+\frac {x^3}{9}+x\right )+c_1 \]