Internal problem ID [4524]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (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);
\[ y \relax (x ) = 1+x +x^{2}+\frac {5}{6} x^{3}+\frac {5}{8} x^{4}+\frac {13}{30} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 30
AsymptoticDSolveValue[{y'[x]-Exp[x]*y[x]==0,{y[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {13 x^5}{30}+\frac {5 x^4}{8}+\frac {5 x^3}{6}+x^2+x+1 \]