Internal problem ID [8389]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 809.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 y^{2} x +64 y^{3}}{\left (4 x -5\right )^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (-125+300*x-240*x^2+64*x^3-80*y(x)^2+64*x*y(x)^2+64*y(x)^3)/(4*x-5)^3,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (-5+4 x \right )+c_{1}\right ) \left (-5+4 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 128
DSolve[y'[x] == (-125 + 300*x - 240*x^2 + 64*x^3 - 80*y[x]^2 + 64*x*y[x]^2 + 64*y[x]^3)/(-5 + 4*x)^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\&,\frac {\log \left (\frac {\frac {192 y(x)}{(4 x-5)^3}+\frac {16}{(4 x-5)^2}}{16 \sqrt [3]{38} \sqrt [3]{\frac {1}{(4 x-5)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(5-4 x)^6}\right )^{2/3} (5-4 x)^4 \log (5-4 x)+c_1,y(x)\right ] \]