60.2.398 problem 976

Internal problem ID [10972]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 976
Date solved : Friday, March 14, 2025 at 02:58:10 AM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 70

ode:=diff(y(x),x) = y(x)/x*(y(x)^2*x^7+y(x)*x^4+x-3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (3\right )+\sqrt {3}\, \ln \left (7\right )-\sqrt {3}\, \ln \left (-\frac {1}{-2+\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+\cos \left (2 \textit {\_Z} \right )}\right )+3 \sqrt {3}\, c_{1} -2 \sqrt {3}\, x -2 \textit {\_Z} \right )\right )-1}{2 x^{3}} \]

✓ Mathematica. Time used: 1.16 (sec). Leaf size: 82

ode=D[y[x],x] == (y[x]*(-3 + x + x^4*y[x] + x^7*y[x]^2))/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 y(x) x^6+x^3}{\sqrt [3]{7} \sqrt [3]{-x^9}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{-1} K[1]}{7^{2/3}}+1}dK[1]=\frac {7^{2/3} \left (-x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]

✓ Sympy. Time used: 10.991 (sec). Leaf size: 58

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**7*y(x)**2 + x**4*y(x) + x - 3)*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - x + \log {\left (x^{3} y{\left (x \right )} \right )} - \frac {\log {\left (x^{6} y^{2}{\left (x \right )} + x^{3} y{\left (x \right )} + 1 \right )}}{2} - \frac {\sqrt {3} \operatorname {atan}{\left (\frac {\sqrt {3} \left (2 x^{3} y{\left (x \right )} + 1\right )}{3} \right )}}{3} = 0 \]