60.2.29 problem 605

Internal problem ID [10603]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 605
Date solved : Sunday, March 30, 2025 at 06:09:47 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {-2+x y}{2 y}\right )\right )}{4 x} \end{align*}

✓ Maple. Time used: 0.101 (sec). Leaf size: 43

ode:=diff(y(x),x) = -1/4*y(x)^2*(2*x-F(-1/2*(-2+x*y(x))/y(x)))/x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2}{x +2 \operatorname {RootOf}\left (F \left (\textit {\_Z} \right )\right )} \\ y &= \frac {2}{2 \operatorname {RootOf}\left (-\ln \left (x \right )-4 \int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_1 \right )+x} \\ \end{align*}

✓ Mathematica. Time used: 0.757 (sec). Leaf size: 145

ode=D[y[x],x] == -1/4*((2*x - F[(1 - (x*y[x])/2)/y[x]])*y[x]^2)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {2 \left (-\frac {K[1]}{2 K[2]}-\frac {1-\frac {1}{2} K[1] K[2]}{K[2]^2}\right ) F''\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )}{F\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )^2}dK[1]-\frac {4}{F\left (\frac {1-\frac {1}{2} x K[2]}{K[2]}\right ) K[2]^2}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]}-\frac {2}{F\left (\frac {1-\frac {1}{2} K[1] y(x)}{y(x)}\right )}\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F = Function("F") 
ode = Eq(Derivative(y(x), x) + (2*x - F((-x*y(x) + 2)/(2*y(x))))*y(x)**2/(4*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-2*x + F((-x*y(x) + 2)/(2*y(x))))*y(x)**2/(4*x) cannot be solved by the factorable group method