54.2.267 problem 845

Internal problem ID [12141]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 845
Date solved : Sunday, October 12, 2025 at 02:22:24 AM
CAS classification : [NONE]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 44

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

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

✓ Mathematica. Time used: 2.992 (sec). Leaf size: 218

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

\begin{align*} y(x)&\to -\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \sqrt [3]{9 x^8+24 x^7+16 x^6+72 x^5+12 (11+6 c_1) x^4+96 c_1 x^3+144 x^2+288 c_1 x+144 c_1{}^2}\\ y(x)&\to \frac {1}{2} \sqrt [3]{\frac {9 x^8}{2}+12 x^7+8 x^6+36 x^5+6 (11+6 c_1) x^4+48 c_1 x^3+72 x^2+144 c_1 x+72 c_1{}^2}\\ y(x)&\to \frac {1}{2} (-1)^{2/3} \sqrt [3]{\frac {9 x^8}{2}+12 x^7+8 x^6+36 x^5+6 (11+6 c_1) x^4+48 c_1 x^3+72 x^2+144 c_1 x+72 c_1{}^2} \end{align*}

✗ Sympy

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

Timed Out