Internal problem ID [8528]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 948.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 68
dsolve(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),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-12 c_{1} {\mathrm e}^{4 \textit {\_Z}}-2 \,{\mathrm e}^{4 \textit {\_Z}} \textit {\_Z} -18 c_{1} {\mathrm e}^{3 \textit {\_Z}}-3 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z} -36 c_{1} {\mathrm e}^{2 \textit {\_Z}}-6 \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} -36 c_{1} {\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+36 c_{1} x +6 \textit {\_Z} x -36\right )} \]
✓ Solution by Mathematica
Time used: 0.467 (sec). Leaf size: 39
DSolve[y'[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),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {36}{y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x}+\log (y(x))=c_1,y(x)\right ] \]