60.2.78 problem 654

Internal problem ID [10652]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 654
Date solved : Wednesday, March 05, 2025 at 12:15:04 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Maple. Time used: 0.204 (sec). Leaf size: 23

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

\[ c_{1} +\frac {3 \ln \left (x +1\right )}{2}-\sqrt {x^{2}+3 y} = 0 \]

✓ Mathematica. Time used: 0.435 (sec). Leaf size: 37

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

\[ y(x)\to \frac {1}{12} \left (-4 x^2+9 \log ^2(x+1)-18 c_1 \log (x+1)+9 c_1{}^2\right ) \]

✓ Sympy. Time used: 1.247 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - \frac {x^{2}}{3} + \frac {3 \left (C_{1} + \log {\left (x + 1 \right )}\right )^{2}}{4} \]