Internal problem ID [413]
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 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+diff(y(x),x)-2*y(x)=0,y(0) = 1, D(y)(0) = -2],y(x),type='series',x=0);
\[ y \relax (x ) = 1-2 x +2 x^{2}-\frac {4}{3} x^{3}+\frac {2}{3} x^{4}-\frac {4}{15} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{y''[x]+y'[x]-2*y[x]==0,{y[0]==1,y'[0]==-2}},y[x],{x,0,5}]
\[ y(x)\to -\frac {4 x^5}{15}+\frac {2 x^4}{3}-\frac {4 x^3}{3}+2 x^2-2 x+1 \]