60.2.396 problem 974

Internal problem ID [10970]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 974
Date solved : Wednesday, March 05, 2025 at 01:33:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=y^{3}-3 x^{2} y^{2}+3 y x^{4}-x^{6}+2 x \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 57

ode:=diff(y(x),x) = y(x)^3-3*x^2*y(x)^2+3*y(x)*x^4-x^6+2*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 46

ode=D[y[x],x] == 2*x - x^6 + 3*x^4*y[x] - 3*x^2*y[x]^2 + y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.029 (sec). Leaf size: 61

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6 - 3*x**4*y(x) + 3*x**2*y(x)**2 - 2*x - y(x)**3 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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