Internal problem ID [8546]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 966.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {1296 y}{216-432 x y-1944 y^{4}-612 y^{5}-1296 y-648 x^{2} y^{2}-324 x^{2} y^{3}+216 x^{3}-1728 y^{3}+216 x^{2}-2376 y^{2}-648 x^{2} y+1080 x y^{3}+216 x y^{2}-882 y^{6}+1152 x y^{4}-846 y^{7}-315 y^{9}-570 y^{8}-216 x^{2} y^{4}+72 y^{8} x +216 y^{7} x +1080 y^{5} x +594 x y^{6}-126 y^{10}-8 y^{12}-36 y^{11}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.048 (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)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-\textit {\_Z} -6 \left (\int _{}^{x -\frac {{\mathrm e}^{4 \textit {\_Z}}}{3}-\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.534 (sec). Leaf size: 292
DSolve[y'[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]
\[ \text {Solve}\left [72 \text {RootSum}\left [-216 \text {$\#$1}^3+216 \text {$\#$1}^2 y(x)^4+324 \text {$\#$1}^2 y(x)^3+648 \text {$\#$1}^2 y(x)^2+648 \text {$\#$1}^2 y(x)-216 \text {$\#$1}^2-72 \text {$\#$1} y(x)^8-216 \text {$\#$1} y(x)^7-594 \text {$\#$1} y(x)^6-1080 \text {$\#$1} y(x)^5-1152 \text {$\#$1} y(x)^4-1080 \text {$\#$1} y(x)^3-216 \text {$\#$1} y(x)^2+432 \text {$\#$1} y(x)+8 y(x)^{12}+36 y(x)^{11}+126 y(x)^{10}+315 y(x)^9+570 y(x)^8+846 y(x)^7+882 y(x)^6+612 y(x)^5+216 y(x)^4-216 y(x)^3-216 y(x)^2-216\&,\frac {\log (x-\text {$\#$1})}{36 \text {$\#$1}^2-24 \text {$\#$1} y(x)^4-36 \text {$\#$1} y(x)^3-72 \text {$\#$1} y(x)^2-72 \text {$\#$1} y(x)+24 \text {$\#$1}+4 y(x)^8+12 y(x)^7+33 y(x)^6+60 y(x)^5+64 y(x)^4+60 y(x)^3+12 y(x)^2-24 y(x)}\&\right ]+\log (y(x))=c_1,y(x)\right ] \]