54.2.144 problem 721

Internal problem ID [12018]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 721
Date solved : Tuesday, September 30, 2025 at 11:56:32 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(y(x),x) = 1/36*(18*x^(3/2)+36*y(x)^2-12*x^3*y(x)+x^6)*x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{6}-\frac {3}{2 x^{{3}/{2}}-3 c_1} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 38

ode=D[y[x],x] == (Sqrt[x]*(18*x^(3/2) + x^6 - 12*x^3*y[x] + 36*y[x]^2))/36; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3}{6}+\frac {1}{-\frac {2 x^{3/2}}{3}+c_1}\\ y(x)&\to \frac {x^3}{6} \end{align*}

✓ Sympy. Time used: 0.764 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x)*(18*x**(3/2) + x**6 - 12*x**3*y(x) + 36*y(x)**2)/36 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x^{3} + 2 x^{\frac {9}{2}} - 18}{6 \left (C_{1} + 2 x^{\frac {3}{2}}\right )} \]