54.2.387 problem 966

Internal problem ID [12261]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 966
Date solved : Wednesday, October 01, 2025 at 01:24:45 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=-\frac {1296 y}{216+216 x^{2}+216 x^{3}+216 y^{7} x +1080 y^{5} x -216 x^{2} y^{4}+594 x y^{6}+1080 x y^{3}-432 x y-324 x^{2} y^{3}-648 x^{2} y^{2}+1152 x y^{4}-648 x^{2} y+216 x y^{2}+72 y^{8} x -126 y^{10}-315 y^{9}-8 y^{12}-36 y^{11}-570 y^{8}-846 y^{7}-612 y^{5}-882 y^{6}-1944 y^{4}-1728 y^{3}-2376 y^{2}-1296 y} \end{align*}

✓ Maple. Time used: 0.114 (sec). Leaf size: 50

ode:=diff(y(x),x) = -1296*y(x)/(216-1944*y(x)^4-1728*y(x)^3-648*x^2*y(x)-882*y(x)^6+216*x*y(x)^2+1152*x*y(x)^4-216*y(x)^4*x^2-126*y(x)^10-8*y(x)^12-36*y(x)^11+1080*x*y(x)^3-432*x*y(x)-2376*y(x)^2-612*y(x)^5-846*y(x)^7-570*y(x)^8-315*y(x)^9+72*y(x)^8*x+216*y(x)^7*x+1080*y(x)^5*x+594*x*y(x)^6-324*x^2*y(x)^3-648*x^2*y(x)^2+216*x^2+216*x^3-1296*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -6 \int _{}^{x -\frac {{\mathrm e}^{4 \textit {\_Z}}}{3}-\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} +c_1 \right )} \]

✓ Mathematica. Time used: 0.473 (sec). Leaf size: 749

ode=D[y[x],x] == (-1296*y[x])/(216 + 216*x^2 + 216*x^3 - 1296*y[x] - 432*x*y[x] - 648*x^2*y[x] - 2376*y[x]^2 + 216*x*y[x]^2 - 648*x^2*y[x]^2 - 1728*y[x]^3 + 1080*x*y[x]^3 - 324*x^2*y[x]^3 - 1944*y[x]^4 + 1152*x*y[x]^4 - 216*x^2*y[x]^4 - 612*y[x]^5 + 1080*x*y[x]^5 - 882*y[x]^6 + 594*x*y[x]^6 - 846*y[x]^7 + 216*x*y[x]^7 - 570*y[x]^8 + 72*x*y[x]^8 - 315*y[x]^9 - 126*y[x]^10 - 36*y[x]^11 - 8*y[x]^12); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {216 \left (8 K[2]^3+9 K[2]^2+12 K[2]+6\right )}{8 K[2]^{12}+36 K[2]^{11}+126 K[2]^{10}+315 K[2]^9-72 x K[2]^8+570 K[2]^8-216 x K[2]^7+846 K[2]^7-594 x K[2]^6+882 K[2]^6-1080 x K[2]^5+612 K[2]^5+216 x^2 K[2]^4-1152 x K[2]^4+216 K[2]^4+324 x^2 K[2]^3-1080 x K[2]^3-216 K[2]^3+648 x^2 K[2]^2-216 x K[2]^2-216 K[2]^2+648 x^2 K[2]+432 x K[2]-216 x^3-216 x^2-216}-\int _1^x-\frac {1296 \left (-96 K[2]^{11}-396 K[2]^{10}-1260 K[2]^9-2835 K[2]^8+576 K[1] K[2]^7-4560 K[2]^7+1512 K[1] K[2]^6-5922 K[2]^6+3564 K[1] K[2]^5-5292 K[2]^5+5400 K[1] K[2]^4-3060 K[2]^4-864 K[1]^2 K[2]^3+4608 K[1] K[2]^3-864 K[2]^3-972 K[1]^2 K[2]^2+3240 K[1] K[2]^2+648 K[2]^2-1296 K[1]^2 K[2]+432 K[1] K[2]+432 K[2]-648 K[1]^2-432 K[1]\right )}{\left (-8 K[2]^{12}-36 K[2]^{11}-126 K[2]^{10}-315 K[2]^9+72 K[1] K[2]^8-570 K[2]^8+216 K[1] K[2]^7-846 K[2]^7+594 K[1] K[2]^6-882 K[2]^6+1080 K[1] K[2]^5-612 K[2]^5-216 K[1]^2 K[2]^4+1152 K[1] K[2]^4-216 K[2]^4-324 K[1]^2 K[2]^3+1080 K[1] K[2]^3+216 K[2]^3-648 K[1]^2 K[2]^2+216 K[1] K[2]^2+216 K[2]^2-648 K[1]^2 K[2]-432 K[1] K[2]+216 K[1]^3+216 K[1]^2+216\right )^2}dK[1]+\frac {1}{K[2]}\right )dK[2]+\int _1^x\frac {1296}{-8 y(x)^{12}-36 y(x)^{11}-126 y(x)^{10}-315 y(x)^9+72 K[1] y(x)^8-570 y(x)^8+216 K[1] y(x)^7-846 y(x)^7+594 K[1] y(x)^6-882 y(x)^6+1080 K[1] y(x)^5-612 y(x)^5-216 K[1]^2 y(x)^4+1152 K[1] y(x)^4-216 y(x)^4-324 K[1]^2 y(x)^3+1080 K[1] y(x)^3+216 y(x)^3-648 K[1]^2 y(x)^2+216 K[1] y(x)^2+216 y(x)^2-648 K[1]^2 y(x)-432 K[1] y(x)+216 K[1]^3+216 K[1]^2+216}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 1296*y(x)/(216*x**3 - 216*x**2*y(x)**4 - 324*x**2*y(x)**3 - 648*x**2*y(x)**2 - 648*x**2*y(x) + 216*x**2 + 72*x*y(x)**8 + 216*x*y(x)**7 + 594*x*y(x)**6 + 1080*x*y(x)**5 + 1152*x*y(x)**4 + 1080*x*y(x)**3 + 216*x*y(x)**2 - 432*x*y(x) - 8*y(x)**12 - 36*y(x)**11 - 126*y(x)**10 - 315*y(x)**9 - 570*y(x)**8 - 846*y(x)**7 - 882*y(x)**6 - 612*y(x)**5 - 1944*y(x)**4 - 1728*y(x)**3 - 2376*y(x)**2 - 1296*y(x) + 216),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - 1296*y(x)/(-216*x**3 + 216*x**2*y(x)**4 + 324*x**2*y(x)**3 + 648*x**2*y(x)**2 + 648*x**2*y(x) - 216*x**2 - 72*x*y(x)**8 - 216*x*y(x)**7 - 594*x*y(x)**6 - 1080*x*y(x)**5 - 1152*x*y(x)**4 - 1080*x*y(x)**3 - 216*x*y(x)**2 + 432*x*y(x) + 8*y(x)**12 + 36*y(x)**11 + 126*y(x)**10 + 315*y(x)**9 + 570*y(x)**8 + 846*y(x)**7 + 882*y(x)**6 + 612*y(x)**5 + 1944*y(x)**4 + 1728*y(x)**3 + 2376*y(x)**2 + 1296*y(x) - 216) cannot be solved by the factorable group method