Internal problem ID [411]
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 20.
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 initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)-4*y(x)=0,y(0) = 2, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = 2+4 x^{2}+\frac {4}{3} x^{4}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 17
AsymptoticDSolveValue[{y''[x]-4*y[x]==0,{y[0]==2,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {4 x^4}{3}+4 x^2+2 \]