60.2.70 problem 646

Internal problem ID [10644]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 646
Date solved : Wednesday, March 05, 2025 at 12:13:56 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \end{align*}

✓ Maple. Time used: 0.254 (sec). Leaf size: 23

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

\[ c_{1} -3 \ln \left (x +1\right )-\sqrt {x^{3}-6 y} = 0 \]

✓ Mathematica. Time used: 0.482 (sec). Leaf size: 35

ode=D[y[x],x] == (x^2/2 + x^3/2 + Sqrt[x^3 - 6*y[x]])/(1 + x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{6} \left (x^3-9 \log ^2(x+1)+18 c_1 \log (x+1)-9 c_1{}^2\right ) \]

✓ Sympy. Time used: 1.273 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**3 + x**2 + 2*sqrt(x**3 - 6*y(x)))/(2*(x + 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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