75.12.26 problem 300

Internal problem ID [16821]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 300
Date solved : Monday, March 31, 2025 at 03:23:03 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }-1&={\mathrm e}^{x +2 y} \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 25

ode:=diff(y(x),x)-1 = exp(2*y(x)+x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{2}+\frac {\ln \left (3\right )}{2}+\frac {\ln \left (\frac {1}{{\mathrm e}^{-3 x} c_1 -2}\right )}{2} \]

✓ Mathematica. Time used: 1.22 (sec). Leaf size: 26

ode=D[y[x],x]-1==Exp[x+2*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x-\frac {1}{2} \log \left (-\frac {2}{3} \left (e^{3 x}+3 c_1\right )\right ) \]

✓ Sympy. Time used: 1.084 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x + 2*y(x)) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {\log {\left (\frac {e^{2 x}}{C_{1} - e^{3 x}} \right )}}{2} - \log {\left (2 \right )} + \frac {\log {\left (6 \right )}}{2}, \ y{\left (x \right )} = \log {\left (- \frac {\sqrt {6} \sqrt {\frac {e^{2 x}}{C_{1} - e^{3 x}}}}{2} \right )}\right ] \]