4.3.32 \(y'(x)=e^{y(x)}+x\)

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 = 0.0545513 (sec), leaf count = 40

\[\left \{\left \{y(x)\to \frac {1}{2} \left (x^2-2 \log \left (-c_1-\sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )\right )\right )\right \}\right \}\]

Maple
cpu = 0.188 (sec), leaf count = 33

\[ \left \{ {\it \_C1}-{\frac {i}{2}}\sqrt {\pi }\sqrt {2}{\it Erf} \left ({\frac {i}{2}}\sqrt {2}x \right ) +{{\rm e}^{-y \relax (x ) +{\frac {{x}^{2}}{2}}}}=0 \right \} \] 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),'implicit')

Maple raw output

_C1-1/2*I*Pi^(1/2)*2^(1/2)*erf(1/2*I*2^(1/2)*x)+exp(-y(x)+1/2*x^2) = 0