Internal problem ID [4529]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {w^{\prime }+x w-{\mathrm e}^{x}=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: 31
Order:=6; dsolve(diff(w(x),x)+x*w(x)=exp(x),w(x),type='series',x=0);
\[ w \relax (x ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) w \relax (0)+x +\frac {x^{2}}{2}-\frac {x^{3}}{6}-\frac {x^{4}}{12}+\frac {x^{5}}{24}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 52
AsymptoticDSolveValue[w'[x]-x*w[x]==Exp[x],w[x],{x,0,5}]
\[ w(x)\to \frac {13 x^5}{120}+\frac {x^4}{6}+\frac {x^3}{2}+\frac {x^2}{2}+c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right )+x \]