10.13.9 problem 11

Internal problem ID [1369]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:56:15 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-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: 39

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

\[ y = \left (1+\frac {1}{6} x^{2}+\frac {1}{24} x^{4}\right ) y \left (0\right )+\left (x +\frac {2}{9} x^{3}+\frac {8}{135} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 70

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

\[ y(x)\to c_1 \left (\frac {13 x^5}{1080}+\frac {x^4}{36}+\frac {x^3}{18}+\frac {x^2}{6}+1\right )+c_2 \left (\frac {49 x^5}{1080}+\frac {7 x^4}{72}+\frac {2 x^3}{9}+\frac {x^2}{2}+x\right ) \]