54.2.345 problem 924

Internal problem ID [12219]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 924
Date solved : Wednesday, October 01, 2025 at 01:14:30 AM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 46

ode:=diff(y(x),x) = -(-1/2*ln(y(x))^2/x-_F1(x))/ln(y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= {\mathrm e}^{\sqrt {2}\, \sqrt {x \left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x +c_1 \right )}} \\ y &= {\mathrm e}^{-\sqrt {2}\, \sqrt {x \left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x +c_1 \right )}} \\ \end{align*}

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 79

ode=D[y[x],x] == ((F1[x] + Log[y[x]]^2/(2*x))*y[x])/Log[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 7.599 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq((-F1(x) - log(y(x))**2/(2*x))*y(x)/log(y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = e^{- \sqrt {2} \sqrt {x \left (C_{1} + \int \frac {F_{1}{\left (x \right )}}{x}\, dx\right )}}, \ y{\left (x \right )} = e^{\sqrt {2} \sqrt {x \left (C_{1} + \int \frac {F_{1}{\left (x \right )}}{x}\, dx\right )}}\right ] \]