5.14 problem 129

Internal problem ID [2878]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 5
Problem number: 129.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]

Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{y}-x=0} \end {gather*}

Solution by Maple

Time used: 0.009 (sec). Leaf size: 34

dsolve(diff(y(x),x) = x+exp(y(x)),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{2}}{2}-\ln \left (\frac {i \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, x}{2}\right )}{2}-c_{1}\right ) \]

Solution by Mathematica

Time used: 0.459 (sec). Leaf size: 40

DSolve[y'[x]==x+Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} 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 ) \\ \end{align*}