Internal problem ID [3386]
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)]`]]
\[ \boxed {y^{\prime }-{\mathrm e}^{y}=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x) = x+exp(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}+\ln \left (2\right )-\ln \left (i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )-2 c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.491 (sec). Leaf size: 40
DSolve[y'[x]==x+Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x^2-2 \log \left (-\sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-c_1\right )\right ) \]