54.1.335 problem 342

Internal problem ID [11649]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 342
Date solved : Tuesday, September 30, 2025 at 09:58:30 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*diff(y(x),x)+y(x))+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\ln \left (5\right )+\ln \left (-\ln \left (x \right )+c_1 \right )}{x} \]

✓ Mathematica. Time used: 60.261 (sec). Leaf size: 163

ode=1 + (2/E^(x*y[x]) + 3*E^(x*y[x]))*x*(y[x] + x*D[y[x],x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\text {arccosh}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\\ y(x)&\to \frac {\text {arccosh}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\\ y(x)&\to -\frac {\text {arccosh}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\\ y(x)&\to \frac {\text {arccosh}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x} \end{align*}

✓ Sympy. Time used: 1.141 (sec). Leaf size: 73

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x*Derivative(y(x), x) + y(x))*(3*exp(x*y(x)) + 2*exp(-x*y(x))) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {\log {\left (- \frac {C_{1}}{6} - \frac {\sqrt {C_{1}^{2} + 2 C_{1} \log {\left (x \right )} + \log {\left (x \right )}^{2} + 24}}{6} - \frac {\log {\left (x \right )}}{6} \right )}}{x}, \ y{\left (x \right )} = \frac {\log {\left (- \frac {C_{1}}{6} + \frac {\sqrt {C_{1}^{2} + 2 C_{1} \log {\left (x \right )} + \log {\left (x \right )}^{2} + 24}}{6} - \frac {\log {\left (x \right )}}{6} \right )}}{x}\right ] \]