85.33.75 problem 76

Internal problem ID [22698]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 76
Date solved : Thursday, October 02, 2025 at 09:10:58 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=exp(2*x-y(x))+exp(y(x)-2*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (-\frac {{\mathrm e}^{4 x}}{2}-2 c_1 \right )}{2} \]

✓ Mathematica. Time used: 0.761 (sec). Leaf size: 24

ode=Exp[2*x-y[x]]+Exp[y[x]-2*x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \log \left (-\frac {e^{4 x}}{2}+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.405 (sec). Leaf size: 37

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

\[ \left [ y{\left (x \right )} = \log {\left (- \sqrt {C_{1} - 2 e^{4 x}} \right )} - \log {\left (2 \right )}, \ y{\left (x \right )} = \frac {\log {\left (C_{1} - 2 e^{4 x} \right )}}{2} - \log {\left (2 \right )}\right ] \]