Internal problem ID [6142]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=8; dsolve((1+x^2)*diff(y(x),x$2)+10*x*diff(y(x),x)+20*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-84 x^{6}+35 x^{4}-10 x^{2}+1\right ) y \relax (0)+\left (-30 x^{7}+14 x^{5}-5 x^{3}+x \right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
AsymptoticDSolveValue[(1+x^2)*y''[x]+10*x*y'[x]+20*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-30 x^7+14 x^5-5 x^3+x\right )+c_1 \left (-84 x^6+35 x^4-10 x^2+1\right ) \]