60.1.72 problem 73

Internal problem ID [10086]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 73
Date solved : Sunday, March 30, 2025 at 03:13:42 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 91

ode:=diff(y(x),x)-((a__3*x^3+a__2*x^2+a__1*x+a__0)/(a__3*y(x)^3+a__2*y(x)^2+a__1*y(x)+a__0))^(2/3) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \int _{}^{y}\left (\textit {\_a}^{3} a_{3} +\textit {\_a}^{2} a_{2} +\textit {\_a} a_{1} +a_{0} \right )^{{2}/{3}}d \textit {\_a} -\left (a_{3} y^{3}+a_{2} y^{2}+a_{1} y+a_{0} \right )^{{2}/{3}} \int _{}^{x}\left (\frac {\textit {\_a}^{3} a_{3} +\textit {\_a}^{2} a_{2} +\textit {\_a} a_{1} +a_{0}}{a_{3} y^{3}+a_{2} y^{2}+a_{1} y+a_{0}}\right )^{{2}/{3}}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 21.123 (sec). Leaf size: 733

ode=D[y[x],x] - ((a3*x^3+a2*x^2+a1*x+a0)/(a3*y[x]^3+a2*y[x]^2+a1*y[x]+a0))^(2/3)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a__0 = symbols("a__0") 
a__1 = symbols("a__1") 
a__2 = symbols("a__2") 
a__3 = symbols("a__3") 
y = Function("y") 
ode = Eq(-((a__0 + a__1*x + a__2*x**2 + a__3*x**3)/(a__0 + a__1*y(x) + a__2*y(x)**2 + a__3*y(x)**3))**(2/3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out