60.1.259 problem 264

Internal problem ID [10273]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 264
Date solved : Sunday, March 30, 2025 at 03:36:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.288 (sec). Leaf size: 37

ode:=2*x*(x^3*y(x)+1)*diff(y(x),x)+(3*x^3*y(x)-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{98}-14 c_1 \,\textit {\_Z}^{77}+49 c_1 \,\textit {\_Z}^{56}-9 x^{7}\right )^{21}-7}{3 x^{3}} \]

✓ Mathematica. Time used: 0.279 (sec). Leaf size: 76

ode=2*x*(x^3*y[x]+1)*D[y[x],x]+(3*x^3*y[x]-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [(-110)^{2/3} \log (x)+72 c_1=72 \int _1^{\frac {(-1)^{2/3} \left (x^3 y(x)-11\right )}{\sqrt [3]{110} \left (y(x) x^3+1\right )}}\frac {1}{K[1]^3+\frac {111 \sqrt [3]{-1} K[1]}{110^{2/3}}+1}dK[1],y(x)\right ] \]

✓ Sympy. Time used: 0.615 (sec). Leaf size: 31

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

\[ - \log {\left (x \right )} + \frac {2 \log {\left (x^{3} y{\left (x \right )} \right )}}{7} + \frac {8 \log {\left (x^{3} y{\left (x \right )} + \frac {7}{3} \right )}}{21} = C_{1} \]