36.6.14 problem 14

Internal problem ID [6375]
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 : 14
Date solved : Monday, January 27, 2025 at 01:58:25 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

Order:=6; 
dsolve([diff(y(x),x)-exp(x)*y(x)=0,y(0) = 1],y(x),type='series',x=0);
 

\[ y = 1+x +x^{2}+\frac {5}{6} x^{3}+\frac {5}{8} x^{4}+\frac {13}{30} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 30

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

\[ y(x)\to \frac {13 x^5}{30}+\frac {5 x^4}{8}+\frac {5 x^3}{6}+x^2+x+1 \]