Internal problem ID [422]
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 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}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 34
Order:=6; dsolve((x^2+3)*diff(y(x),x$2)-7*x*diff(y(x),x)+16*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {8}{3} x^{2}+\frac {8}{27} x^{4}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{3}+\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[(x^2+3)*y''[x]-7*x*y'[x]+16*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{120}-\frac {x^3}{2}+x\right )+c_1 \left (\frac {8 x^4}{27}-\frac {8 x^2}{3}+1\right ) \]