Internal problem ID [8548]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 970.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {y^{\prime }+\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 y-648 y x^{2}-216 x^{2} y^{4}-1944 x y^{2}+2808 y^{4}+2484 y^{6}+216 x^{3}-1296 y x +1728 y^{3}-1296 y^{2}-648 x^{2} y^{2}-648 y^{3} x +72 y^{8} x -126 y^{10}-315 y^{9}-8 y^{12}-36 y^{11}+1080 y^{5} x +216 y^{7} x +594 x y^{6}+594 y^{7}-432 x y^{4}-324 x^{2} y^{3}+4428 y^{5}-18 y^{8}}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 183
dsolve(diff(y(x),x) = -216*y(x)*(-2*y(x)^4-3*y(x)^3-6*y(x)^2-6*y(x)+6*x+6)/(72*y(x)^8*x+216*y(x)^7*x+1080*y(x)^5*x+2484*y(x)^6-216*x^2*y(x)^4+594*x*y(x)^6-648*x*y(x)^3-1296*x*y(x)-324*x^2*y(x)^3-648*x^2*y(x)^2-432*x*y(x)^4-648*x^2*y(x)-1944*x*y(x)^2+4428*y(x)^5+2808*y(x)^4-1296*y(x)+1728*y(x)^3+216*x^3-1296*y(x)^2-126*y(x)^10-315*y(x)^9-8*y(x)^12-36*y(x)^11+594*y(x)^7-18*y(x)^8),y(x), singsol=all)
\begin{align*} x -\frac {2 \ln \left (y \left (x \right )\right ) y \left (x \right )^{4}-72 c_{1} y \left (x \right )^{4}+3 \ln \left (y \left (x \right )\right ) y \left (x \right )^{3}-108 c_{1} y \left (x \right )^{3}+6 y \left (x \right )^{2} \ln \left (y \left (x \right )\right )-216 c_{1} y \left (x \right )^{2}+6 y \left (x \right ) \ln \left (y \left (x \right )\right )-216 c_{1} y \left (x \right )-6 \sqrt {3 \ln \left (y \left (x \right )\right )-108 c_{1} +9}+18}{6 \left (-36 c_{1} +\ln \left (y \left (x \right )\right )\right )} = 0 \\ x -\frac {2 \ln \left (y \left (x \right )\right ) y \left (x \right )^{4}-72 c_{1} y \left (x \right )^{4}+3 \ln \left (y \left (x \right )\right ) y \left (x \right )^{3}-108 c_{1} y \left (x \right )^{3}+6 y \left (x \right )^{2} \ln \left (y \left (x \right )\right )-216 c_{1} y \left (x \right )^{2}+6 y \left (x \right ) \ln \left (y \left (x \right )\right )-216 c_{1} y \left (x \right )+6 \sqrt {3 \ln \left (y \left (x \right )\right )-108 c_{1} +9}+18}{6 \left (-36 c_{1} +\ln \left (y \left (x \right )\right )\right )} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.449 (sec). Leaf size: 66
DSolve[y'[x] == (-216*y[x]*(6 + 6*x - 6*y[x] - 6*y[x]^2 - 3*y[x]^3 - 2*y[x]^4))/(216*x^3 - 1296*y[x] - 1296*x*y[x] - 648*x^2*y[x] - 1296*y[x]^2 - 1944*x*y[x]^2 - 648*x^2*y[x]^2 + 1728*y[x]^3 - 648*x*y[x]^3 - 324*x^2*y[x]^3 + 2808*y[x]^4 - 432*x*y[x]^4 - 216*x^2*y[x]^4 + 4428*y[x]^5 + 1080*x*y[x]^5 + 2484*y[x]^6 + 594*x*y[x]^6 + 594*y[x]^7 + 216*x*y[x]^7 - 18*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]
\[ \text {Solve}\left [\frac {36 \left (2 y(x)^4+3 y(x)^3+6 y(x)^2+6 y(x)-6 x-3\right )}{\left (y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x\right )^2}+\log (y(x))=c_1,y(x)\right ] \]