Internal problem ID [392]
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 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 37
AsymptoticDSolveValue[y'[x]==y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right ) \]