Internal problem ID [419]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number: problem 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((x^2+1)*diff(y(x),x$2)+6*x*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (3 x^{4}-2 x^{2}+1\right ) y \relax (0)+\left (x -\frac {5}{3} x^{3}+\frac {7}{3} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 60
AsymptoticDSolveValue[(x^2+1)*y''[x]+6*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (4 x^5-5 x^4+4 x^3-2 x^2+1\right )+c_2 \left (\frac {77 x^5}{15}-\frac {13 x^4}{2}+\frac {16 x^3}{3}-3 x^2+x\right ) \]