29.5.13 problem 129

Internal problem ID [4730]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 129
Date solved : Monday, January 27, 2025 at 09:34:40 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 34

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: 0.528 (sec). Leaf size: 40

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

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