Internal problem ID [403]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page
615
Problem number: problem 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 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: 34
Order:=6; dsolve(diff(y(x),x$2)=4*y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+2 x^{2}+\frac {2}{3} x^{4}\right ) y \relax (0)+\left (x +\frac {2}{3} x^{3}+\frac {2}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[y''[x]==4*y[x],y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {2 x^5}{15}+\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {2 x^4}{3}+2 x^2+1\right ) \]