Internal problem ID [4730]
Book: Advanced Mathemtical 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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (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);
\[ y \relax (x ) = -5 x^{3}+3 x \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 12
AsymptoticDSolveValue[{(1-x^2)*y''[x]-2*x*y'[x]+12*y[x]==0,{y[0]==0,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to 3 x-5 x^3 \]