60.2.343 problem 921

Internal problem ID [10917]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 921
Date solved : Sunday, March 30, 2025 at 07:23:13 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 {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \end{align*}

✓ Maple. Time used: 0.117 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.269 (sec). Leaf size: 91

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

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

✓ Sympy. Time used: 6.095 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq((-F1(x) - log(y(x))/x + log(y(x))/(x*log(x)))*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{- \frac {x \left (- C_{1} - \int \frac {F_{1}{\left (x \right )} \log {\left (x \right )}}{x}\, dx\right )}{\log {\left (x \right )}}} \]