54.2.16 problem 592

Internal problem ID [11890]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 592
Date solved : Sunday, October 12, 2025 at 02:02:17 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 33

ode:=diff(y(x),x) = 1/5*(6*x^3+5*x^(1/2)+5*F(y(x)-2/5*x^3-2*x^(1/2)))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ \int _{\textit {\_b}}^{y}\frac {1}{F \left (\textit {\_a} -\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}d \textit {\_a} -\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.21 (sec). Leaf size: 241

ode=D[y[x],x] == (Sqrt[x] + (6*x^3)/5 + F[-2*Sqrt[x] - (2*x^3)/5 + y[x]])/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}-\frac {F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right ) \int _1^x\left (-\frac {6 F''\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right ) K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2}-\frac {F''\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2 \sqrt {K[1]}}\right )dK[1]+1}{F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right )}dK[2]+\int _1^x\left (\frac {6 K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right )}+\frac {1}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right ) \sqrt {K[1]}}+\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F = Function("F") 
ode = Eq(Derivative(y(x), x) - (5*sqrt(x) + 6*x**3 + 5*F(-2*sqrt(x) - 2*x**3/5 + y(x)))/(5*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -6*x**2/5 + Derivative(y(x), x) - F(-2*sqrt(x) - 2*x**3/5 + y(x))/x - 1/sqrt(x) cannot be solved by the factorable group method