60.2.402 problem 980

Internal problem ID [10976]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 980
Date solved : Wednesday, March 05, 2025 at 01:34:13 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8+2 x}{x^{3}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=diff(y(x),x) = (x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8+2*x)/x^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{\sqrt {c_{1} -2 x}}-\frac {2}{x} \\ y &= \frac {1}{\sqrt {c_{1} -2 x}}-\frac {2}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.237 (sec). Leaf size: 53

ode=D[y[x],x] == (8 + 2*x + 12*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {2+\frac {x}{\sqrt {-2 x+c_1}}}{x} \\ y(x)\to -\frac {2}{x}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {2}{x} \\ \end{align*}

✓ Sympy. Time used: 1.519 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**3*y(x)**3 + 6*x**2*y(x)**2 + 12*x*y(x) + 2*x + 8)/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {- 2 C_{1} - \frac {\sqrt {2} x \sqrt {- C_{1} - x}}{2} - 2 x}{x \left (C_{1} + x\right )}, \ y{\left (x \right )} = \frac {- 2 C_{1} + \frac {\sqrt {2} x \sqrt {- C_{1} - x}}{2} - 2 x}{x \left (C_{1} + x\right )}\right ] \]