88.12.23 problem 25

Internal problem ID [24079]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 25
Date solved : Thursday, October 02, 2025 at 09:57:29 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=exp(2*x+3*y(x))+exp(4*x-5*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\ln \left (-4 \,{\mathrm e}^{-2 x}+8 c_1 \right )}{8} \]

✓ Mathematica. Time used: 0.85 (sec). Leaf size: 22

ode=Exp[2*x+3*y[x]]+Exp[4*x-5*y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{8} \log \left (-4 e^{-2 x}-8 c_1\right ) \end{align*}

✓ Sympy. Time used: 30.603 (sec). Leaf size: 236

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(exp(2*x + 3*y(x)) + exp(4*x - 5*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \log {\left (- i \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 4}} \right )}, \ y{\left (x \right )} = \log {\left (i \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 4}} \right )}, \ y{\left (x \right )} = \log {\left (- \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 4}} \right )}, \ y{\left (x \right )} = \frac {\log {\left (- \frac {e^{2 x}}{C_{1} e^{2 x} + 4} \right )}}{8}, \ y{\left (x \right )} = \log {\left (\sqrt [4]{2} \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 1}} \left (- \frac {1}{2} - \frac {i}{2}\right ) \right )}, \ y{\left (x \right )} = \log {\left (\sqrt [4]{2} i \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 1}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (x \right )} = \log {\left (- \sqrt [4]{2} i \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 1}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (x \right )} = \log {\left (\sqrt [4]{2} \sqrt [8]{- \frac {e^{2 x}}{C_{1} e^{2 x} + 1}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}\right ] \]