60.2.209 problem 785

Internal problem ID [10783]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 785
Date solved : Sunday, March 30, 2025 at 06:39:04 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=-\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 24

ode:=diff(y(x),x) = -(ln(x)-sinh(x)*x^2-2*sinh(x)*x*y(x)-sinh(x)-sinh(x)*y(x)^2)/ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x -\tan \left (c_1 -\int \frac {\sinh \left (x \right )}{\ln \left (x \right )}d x \right ) \]

✓ Mathematica. Time used: 0.462 (sec). Leaf size: 29

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

\[ y(x)\to -x+\tan \left (\int _1^x\frac {\sinh (K[5])}{\log (K[5])}dK[5]+c_1\right ) \]

✗ Sympy

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

IndexError : Index out of range: a[1]