60.2.389 problem 966
Internal
problem
ID
[10976]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
966
Date
solved
:
Monday, January 27, 2025 at 10:36:49 PM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=-\frac {1296 y}{216+216 x^{3}+216 x y^{2}-648 x^{2} y-1296 y+216 x^{2}+1080 x y^{3}-324 x^{2} y^{3}-1728 y^{3}-432 y x -126 y^{10}-315 y^{9}-8 y^{12}-36 y^{11}-2376 y^{2}-570 y^{8}+72 y^{8} x +216 y^{7} x -882 y^{6}-846 y^{7}-612 y^{5}-216 x^{2} y^{4}-1944 y^{4}+1152 x y^{4}-648 x^{2} y^{2}+594 x y^{6}+1080 y^{5} x} \end{align*}
✓ Solution by Maple
Time used: 0.237 (sec). Leaf size: 50
dsolve(diff(y(x),x) = -1296*y(x)/(216+72*y(x)^8*x+216*y(x)^7*x+1080*y(x)^5*x-882*y(x)^6-216*x^2*y(x)^4+594*x*y(x)^6+1080*x*y(x)^3-432*x*y(x)-324*x^2*y(x)^3-648*x^2*y(x)^2+1152*x*y(x)^4-648*x^2*y(x)+216*x*y(x)^2-612*y(x)^5-1944*y(x)^4-1296*y(x)-1728*y(x)^3+216*x^3-2376*y(x)^2+216*x^2-126*y(x)^10-315*y(x)^9-8*y(x)^12-36*y(x)^11-846*y(x)^7-570*y(x)^8),y(x), singsol=all)
\[
y = {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -6 \left (\int _{}^{-\frac {{\mathrm e}^{4 \textit {\_Z}}}{3}-\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}}+x}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1} \right )}
\]
✓ Solution by Mathematica
Time used: 0.756 (sec). Leaf size: 749
DSolve[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),y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {216 \left (8 K[2]^3+9 K[2]^2+12 K[2]+6\right )}{8 K[2]^{12}+36 K[2]^{11}+126 K[2]^{10}+315 K[2]^9-72 x K[2]^8+570 K[2]^8-216 x K[2]^7+846 K[2]^7-594 x K[2]^6+882 K[2]^6-1080 x K[2]^5+612 K[2]^5+216 x^2 K[2]^4-1152 x K[2]^4+216 K[2]^4+324 x^2 K[2]^3-1080 x K[2]^3-216 K[2]^3+648 x^2 K[2]^2-216 x K[2]^2-216 K[2]^2+648 x^2 K[2]+432 x K[2]-216 x^3-216 x^2-216}-\int _1^x-\frac {1296 \left (-96 K[2]^{11}-396 K[2]^{10}-1260 K[2]^9-2835 K[2]^8+576 K[1] K[2]^7-4560 K[2]^7+1512 K[1] K[2]^6-5922 K[2]^6+3564 K[1] K[2]^5-5292 K[2]^5+5400 K[1] K[2]^4-3060 K[2]^4-864 K[1]^2 K[2]^3+4608 K[1] K[2]^3-864 K[2]^3-972 K[1]^2 K[2]^2+3240 K[1] K[2]^2+648 K[2]^2-1296 K[1]^2 K[2]+432 K[1] K[2]+432 K[2]-648 K[1]^2-432 K[1]\right )}{\left (-8 K[2]^{12}-36 K[2]^{11}-126 K[2]^{10}-315 K[2]^9+72 K[1] K[2]^8-570 K[2]^8+216 K[1] K[2]^7-846 K[2]^7+594 K[1] K[2]^6-882 K[2]^6+1080 K[1] K[2]^5-612 K[2]^5-216 K[1]^2 K[2]^4+1152 K[1] K[2]^4-216 K[2]^4-324 K[1]^2 K[2]^3+1080 K[1] K[2]^3+216 K[2]^3-648 K[1]^2 K[2]^2+216 K[1] K[2]^2+216 K[2]^2-648 K[1]^2 K[2]-432 K[1] K[2]+216 K[1]^3+216 K[1]^2+216\right )^2}dK[1]+\frac {1}{K[2]}\right )dK[2]+\int _1^x\frac {1296}{-8 y(x)^{12}-36 y(x)^{11}-126 y(x)^{10}-315 y(x)^9+72 K[1] y(x)^8-570 y(x)^8+216 K[1] y(x)^7-846 y(x)^7+594 K[1] y(x)^6-882 y(x)^6+1080 K[1] y(x)^5-612 y(x)^5-216 K[1]^2 y(x)^4+1152 K[1] y(x)^4-216 y(x)^4-324 K[1]^2 y(x)^3+1080 K[1] y(x)^3+216 y(x)^3-648 K[1]^2 y(x)^2+216 K[1] y(x)^2+216 y(x)^2-648 K[1]^2 y(x)-432 K[1] y(x)+216 K[1]^3+216 K[1]^2+216}dK[1]=c_1,y(x)\right ]
\]