54.7.100 problem 1712 (book 6.121)

Internal problem ID [12949]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1712 (book 6.121)
Date solved : Friday, October 03, 2025 at 03:50:58 AM
CAS classification : [[_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime } y-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right )&=0 \end{align*}

✓ Maple. Time used: 0.201 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+(tan(x)+cot(x))*y(x)*diff(y(x),x)+(cos(x)^2-n^2*cot(x)^2)*y(x)^2*ln(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {\pi \left (\operatorname {BesselJ}\left (n , \sin \left (x \right )\right ) c_1 -c_2 \operatorname {BesselY}\left (n , \sin \left (x \right )\right )\right )}{2}} \]

✓ Mathematica. Time used: 65.495 (sec). Leaf size: 858

ode=(Cos[x]^2 - n^2*Cot[x]^2)*Log[y[x]]*y[x]^2 + (Cot[x] + Tan[x])*y[x]*D[y[x],x] - D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out