60.2.273 problem 850

Internal problem ID [10847]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 850
Date solved : Sunday, March 30, 2025 at 07:14:19 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \end{align*}

✓ Maple. Time used: 0.119 (sec). Leaf size: 27

ode:=diff(y(x),x) = 1/sin(x)+_F1(y(x)-ln(sin(x))+ln(cos(x)+1)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (\textit {\_a} \right )}d \textit {\_a} +c_1 \right ) \]

✓ Mathematica. Time used: 0.545 (sec). Leaf size: 1438

ode=D[y[x],x] == Csc[x] + F1[Log[1 + Cos[x]] - Log[Sin[x]] + y[x]]; 
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") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq(-F1(y(x) + log(cos(x) + 1) - log(sin(x))) + Derivative(y(x), x) - 1/sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -F1(y(x) + log(cos(x) + 1) - log(sin(x))) + Derivative(y(x), x) - 1/sin(x) cannot be solved by the lie group method