60.2.216 problem 792

Internal problem ID [10790]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 792
Date solved : Sunday, March 30, 2025 at 06:53:48 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 87

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

\[ y = \frac {{\mathrm e}^{-\int \frac {\left (x^{2}+x \right ) \operatorname {sech}\left (\frac {1}{x +1}\right )+x -1}{\left (x -1\right ) x}d x}}{-\int \frac {x \left (x +1\right ) {\mathrm e}^{-\int \frac {\left (x^{2}+x \right ) \operatorname {sech}\left (\frac {1}{x +1}\right )+x -1}{\left (x -1\right ) x}d x} \operatorname {sech}\left (\frac {1}{x +1}\right )}{x -1}d x +c_1} \]

✓ Mathematica. Time used: 0.863 (sec). Leaf size: 238

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

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

✗ Sympy

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

Timed Out