Internal problem ID [15482]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.1 Integration of differential equation in
series. Power series. Exercises page 171
Problem number: 738.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-{\mathrm e}^{y}-y x=0} \] 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: 18
Order:=6; dsolve([diff(y(x),x)=exp(y(x))+x*y(x),y(0) = 0],y(x),type='series',x=0);
\[ y = x +\frac {1}{2} x^{2}+\frac {2}{3} x^{3}+\frac {11}{24} x^{4}+\frac {53}{120} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 33
AsymptoticDSolveValue[{y'[x]==Exp[y[x]]+x*y[x],{y[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {53 x^5}{120}+\frac {11 x^4}{24}+\frac {2 x^3}{3}+\frac {x^2}{2}+x \]