54.2.220 problem 797

Internal problem ID [12094]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 797
Date solved : Wednesday, October 01, 2025 at 12:31:59 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x} \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 191

ode:=diff(y(x),x) = y(x)*(-1-cosh((1+x)/(x-1))*x+cosh((1+x)/(x-1))*x^2*y(x)-cosh((1+x)/(x-1))*x^2+cosh((1+x)/(x-1))*x^3*y(x))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-1-x}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}+{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (\frac {2}{x -1}\right )-3 \,{\mathrm e} \,\operatorname {Ei}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (-\int \left (x +1\right ) {\mathrm e}^{\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-1-x}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}+{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (\frac {2}{x -1}\right )-3 \,{\mathrm e} \,\operatorname {Ei}_{1}\left (-\frac {2}{x -1}\right )} \left (\sinh \left (\frac {x}{x -1}\right ) \sinh \left (\frac {1}{x -1}\right )+\cosh \left (\frac {x}{x -1}\right ) \cosh \left (\frac {1}{x -1}\right )\right )d x +c_1 \right )} \]

✓ Mathematica. Time used: 1.639 (sec). Leaf size: 113

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

\begin{align*} y(x)&\to \frac {\exp \left (\int _1^x\left (-\cosh \left (\frac {K[1]+1}{K[1]-1}\right ) (K[1]+1)-\frac {1}{K[1]}\right )dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\left (-\cosh \left (\frac {K[1]+1}{K[1]-1}\right ) (K[1]+1)-\frac {1}{K[1]}\right )dK[1]\right ) \cosh \left (\frac {K[2]+1}{K[2]-1}\right ) K[2] (K[2]+1)dK[2]+c_1}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out