Internal problem ID [2472]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Additional problems. Section
11.7. page 788
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (4 x^{2}+1\right ) y^{\prime \prime }-8 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: 29
Order:=6; dsolve((1+4*x^2)*diff(y(x),x$2)-8*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (4 x^{2}+1\right ) y \relax (0)+\left (x +\frac {4}{3} x^{3}-\frac {16}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 33
AsymptoticDSolveValue[(1+4*x^2)*y''[x]-8*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (4 x^2+1\right )+c_2 \left (-\frac {16 x^5}{15}+\frac {4 x^3}{3}+x\right ) \]