54.2.369 problem 948

Internal problem ID [12243]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 948
Date solved : Wednesday, October 01, 2025 at 01:21:36 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 x y+60 y^{5}-36 x y^{3}-72 x y^{2}-24 x y^{4}+4 y^{8}+12 y^{7}+33 y^{6}} \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 68

ode:=diff(y(x),x) = -216*y(x)/(-216*y(x)^4-252*y(x)^3-396*y(x)^2-216*y(x)+36*x^2-72*x*y(x)+60*y(x)^5-36*x*y(x)^3-72*x*y(x)^2-24*x*y(x)^4+4*y(x)^8+12*y(x)^7+33*y(x)^6); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (12 c_1 \,{\mathrm e}^{4 \textit {\_Z}}+2 \,{\mathrm e}^{4 \textit {\_Z}} \textit {\_Z} +18 c_1 \,{\mathrm e}^{3 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z} +36 c_1 \,{\mathrm e}^{2 \textit {\_Z}}+6 \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} +36 c_1 \,{\mathrm e}^{\textit {\_Z}}+6 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} -36 c_1 x -6 \textit {\_Z} x +36\right )} \]

✓ Mathematica. Time used: 0.288 (sec). Leaf size: 39

ode=D[y[x],x] == (-216*y[x])/(36*x^2 - 216*y[x] - 72*x*y[x] - 396*y[x]^2 - 72*x*y[x]^2 - 252*y[x]^3 - 36*x*y[x]^3 - 216*y[x]^4 - 24*x*y[x]^4 + 60*y[x]^5 + 33*y[x]^6 + 12*y[x]^7 + 4*y[x]^8); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {36}{y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x}+\log (y(x))=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 216*y(x)/(36*x**2 - 24*x*y(x)**4 - 36*x*y(x)**3 - 72*x*y(x)**2 - 72*x*y(x) + 4*y(x)**8 + 12*y(x)**7 + 33*y(x)**6 + 60*y(x)**5 - 216*y(x)**4 - 252*y(x)**3 - 396*y(x)**2 - 216*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - 216*y(x)/(-36*x**2 + 24*x*y(x)**4 + 36*x*y(x)**3 + 72*x*y(x)**2 + 72*x*y(x) - 4*y(x)**8 - 12*y(x)**7 - 33*y(x)**6 - 60*y(x)**5 + 216*y(x)**4 + 252*y(x)**3 + 396*y(x)**2 + 216*y(x)) cannot be solved by the factorable group method