Internal problem ID [410]
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 19.
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) = 0, y^{\prime }\relax (0) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \relax (x ) = 3 x -2 x^{3}+\frac {2}{5} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]+4*y[x]==0,{y[0]==0,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {2 x^5}{5}-2 x^3+3 x \]