ODE
\[ y'(x)=e^{y(x)}+x \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
Book solution method
Series solution to \(y'(x)=f(x,y(x))\), case \(f(x,y)\) analytic
Mathematica ✓
cpu = 0.293324 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x^2-2 \log \left (-\sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-c_1\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.163 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {x^{2}}{2}-\ln \left (\frac {i \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, x}{2}\right )}{2}-\textit {\_C1} \right )\right ]\] Mathematica raw input
DSolve[y'[x] == E^y[x] + x,y[x],x]
Mathematica raw output
{{y[x] -> (x^2 - 2*Log[-C[1] - Sqrt[Pi/2]*Erfi[x/Sqrt[2]]])/2}}
Maple raw input
dsolve(diff(y(x),x) = x+exp(y(x)), y(x))
Maple raw output
[y(x) = 1/2*x^2-ln(1/2*I*Pi^(1/2)*2^(1/2)*erf(1/2*I*2^(1/2)*x)-_C1)]