36.6.19 problem 22

Internal problem ID [6380]
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
Date solved : Monday, January 27, 2025 at 01:58:31 PM
CAS classification : [_linear]

\begin{align*} w^{\prime }+w x&={\mathrm e}^{x} \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 45

Order:=6; 
dsolve(diff(w(x),x)+x*w(x)=exp(x),w(x),type='series',x=0);
 

\[ w = \left (1-\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) w \left (0\right )+x +\frac {x^{2}}{2}-\frac {x^{3}}{6}-\frac {x^{4}}{12}+\frac {x^{5}}{24}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 52

AsymptoticDSolveValue[D[w[x],x]-x*w[x]==Exp[x],w[x],{x,0,"6"-1}]
 

\[ w(x)\to \frac {13 x^5}{120}+\frac {x^4}{6}+\frac {x^3}{2}+\frac {x^2}{2}+c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right )+x \]