Internal problem ID [2390]
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. Exercises for 11.2. page
739
Problem number: Problem 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime } x -2 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: 32
Order:=6; dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+x^{2}+\frac {1}{2} x^{4}\right ) y \relax (0)+\left (x +\frac {2}{3} x^{3}+\frac {4}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[y''[x]-2*x*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {4 x^5}{15}+\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {x^4}{2}+x^2+1\right ) \]