60.1.335 problem 342
Internal
problem
ID
[10349]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
342
Date
solved
:
Wednesday, March 05, 2025 at 10:31:52 AM
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: 0.008 (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: 60.433 (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: 1.661 (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)
\[
\left [ y{\left (x \right )} = \frac {\log {\left (- \frac {C_{1}}{6} - \frac {\sqrt {C_{1}^{2} + 2 C_{1} \log {\left (x \right )} + \log {\left (x \right )}^{2} + 24}}{6} - \frac {\log {\left (x \right )}}{6} \right )}}{x}, \ y{\left (x \right )} = \frac {\log {\left (- \frac {C_{1}}{6} + \frac {\sqrt {C_{1}^{2} + 2 C_{1} \log {\left (x \right )} + \log {\left (x \right )}^{2} + 24}}{6} - \frac {\log {\left (x \right )}}{6} \right )}}{x}\right ]
\]