Internal problem ID [6548]
Book: A course in Ordinary Differential Equations. by Stephen A. Wirkus, Randall J. Swift. CRC
Press NY. 2015. 2nd Edition
Section: Chapter 8. Series Methods. section 8.2. The Power Series Method. Problems Page
603
Problem number: 3. series method.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-y-{\mathrm e}^{y} x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=8; dsolve([diff(y(x),x)=y(x)+x*exp(y(x)),y(0) = 0],y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{6} x^{4}+\frac {1}{15} x^{5}+\frac {43}{720} x^{6}+\frac {151}{5040} x^{7}+\operatorname {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 46
AsymptoticDSolveValue[{y'[x]==y[x]+x*Exp[y[x]],{y[0]==0}},y[x],{x,0,7}]
\[ y(x)\to \frac {151 x^7}{5040}+\frac {43 x^6}{720}+\frac {x^5}{15}+\frac {x^4}{6}+\frac {x^3}{6}+\frac {x^2}{2} \]