51.1.6 problem 3. direct method

Internal problem ID [8217]
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. direct method
Date solved : Monday, January 27, 2025 at 03:46:12 PM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(x),x)=y(x)+x*exp(y(x)),y(0) = 0],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],x]==y[x]+x*Exp[y[x]],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved