Internal problem ID [4881]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page
174
Problem number: 18.
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 }+30 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 0, y^{\prime }\relax (0) = {\frac {15}{8}}\right ] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
Order:=6; dsolve([(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+30*y(x)=0,y(0) = 0, D(y)(0) = 15/8],y(x),type='series',x=0);
\[ y \relax (x ) = \frac {15}{8} x -\frac {35}{4} x^{3}+\frac {63}{8} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 23
AsymptoticDSolveValue[{(1-x^2)*y''[x]-2*x*y'[x]+30*y[x]==0,{y[0]==0,y'[0]==1875/1000}},y[x],{x,0,5}]
\[ y(x)\to \frac {63 x^5}{8}-\frac {35 x^3}{4}+\frac {15 x}{8} \]