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 : Tuesday, March 04, 2025 at 07:12:02 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

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

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

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

✓ Mathematica. Time used: 0.528 (sec). Leaf size: 40

ode=D[y[x],x]==x+Exp[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.839 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - exp(y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\frac {\sqrt {e^{x^{2}}}}{C_{1} - \int \sqrt {e^{x^{2}}}\, dx} \right )} \]