60.2.333 problem 911

Internal problem ID [10907]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 911
Date solved : Sunday, March 30, 2025 at 07:21:49 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{\csc \left (x \right ) x \left (c_1 +\int \frac {\textit {\_F1} \left (x \right ) \sin \left (x \right )}{x}d x \right )} \]

✓ Mathematica. Time used: 0.737 (sec). Leaf size: 105

ode=D[y[x],x] == (F1[x] + Log[y[x]]/x - Cot[x]*Log[y[x]])*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x\left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}+\frac {2 (\text {F1}(K[1]) \sin (K[1])-\cos (K[1]) \log (y(x)))}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 \sin (x)}{x K[2]}-\int _1^x\left (\frac {2 \sin (K[1])}{K[1]^2 K[2]}-\frac {2 \cos (K[1])}{K[1] K[2]}\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 18.000 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-_F1(x) + log(y(x))*cos(x)/sin(x) - log(y(x))/x)*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{- \frac {x \left (- C_{1} - \int \frac {\operatorname {_F1}{\left (x \right )} \tan {\left (x \right )}}{x \sqrt {\frac {1}{\cos ^{2}{\left (x \right )}}}}\, dx\right ) \sqrt {\frac {1}{\cos ^{2}{\left (x \right )}}}}{\tan {\left (x \right )}}} \]