Internal problem ID [8380]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 800.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 y^{2} x +8 y^{3}}{\left (2 x -b \right )^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (-b^3+6*b^2*x-12*b*x^2+8*x^3-4*y(x)^2*b+8*x*y(x)^2+8*y(x)^3)/(2*x-b)^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (-2 x +b \right )+c_{1}\right ) \left (-2 x +b \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 128
DSolve[y'[x] == (-b^3 + 6*b^2*x - 12*b*x^2 + 8*x^3 - 4*b*y[x]^2 + 8*x*y[x]^2 + 8*y[x]^3)/(-b + 2*x)^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\&,\frac {\log \left (\frac {\frac {4}{(b-2 x)^2}-\frac {24 y(x)}{(b-2 x)^3}}{4 \sqrt [3]{38} \sqrt [3]{\frac {1}{(b-2 x)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(b-2 x)^6}\right )^{2/3} (b-2 x)^4 \log (b-2 x)+c_1,y(x)\right ] \]