60.8.5 problem 1841

Internal problem ID [11766]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1841
Date solved : Sunday, March 30, 2025 at 09:14:36 PM
CAS classification : [[_3rd_order, _exact, _nonlinear]]

\begin{align*} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \end{align*}

✗ Maple

ode:=x^2*diff(diff(diff(y(x),x),x),x)+x*diff(diff(y(x),x),x)+(2*x*y(x)-1)*diff(y(x),x)+y(x)^2-f(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-f[x] + y[x]^2 + (-1 + 2*x*y[x])*D[y[x],x] + x*D[y[x],{x,2}] + x^2*Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) + x*Derivative(y(x), (x, 2)) + (2*x*y(x) - 1)*Derivative(y(x), x) - f(x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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