54.2.143 problem 720

Internal problem ID [12017]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 720
Date solved : Sunday, October 12, 2025 at 02:11:08 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 48

ode:=diff(y(x),x) = x^3*(3*x+3+(9*x^4-4*y(x)^3)^(1/2))/(1+x)/y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \int _{\textit {\_b}}^{y}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-c_1 = 0 \]

✓ Mathematica. Time used: 3.362 (sec). Leaf size: 175

ode=D[y[x],x] == (x^3*(3 + 3*x + Sqrt[9*x^4 - 4*y[x]^3]))/((1 + x)*y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \left (\int \frac {x^3}{x+1} \, dx\right )^2+8 c_1 \int \frac {x^3}{x+1} \, dx-4 c_1{}^2}\\ y(x)&\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \left (\int \frac {x^3}{x+1} \, dx\right )^2+8 c_1 \int \frac {x^3}{x+1} \, dx-4 c_1{}^2}\\ y(x)&\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \left (\int \frac {x^3}{x+1} \, dx\right )^2+8 c_1 \int \frac {x^3}{x+1} \, dx-4 c_1{}^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*(3*x + sqrt(9*x**4 - 4*y(x)**3) + 3)/((x + 1)*y(x)**2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out