42.1.4 problem 3.6 (c)

Internal problem ID [6826]
Book : Advanced Mathematical Methods for Scientists and Engineers, Bender and Orszag. Springer October 29, 1999
Section : Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page 136
Problem number : 3.6 (c)
Date solved : Monday, January 27, 2025 at 02:31:14 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

Order:=6; 
dsolve([(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+12*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x),type='series',x=0);
 

\[ y = -5 x^{3}+3 x \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 12

AsymptoticDSolveValue[{(1-x^2)*D[y[x],{x,2}]-2*x*D[y[x],x]+12*y[x]==0,{y[0]==0,Derivative[1][y][0] ==3}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to 3 x-5 x^3 \]