Internal problem ID [8523]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 943.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 y x^{4}-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 40
dsolve(diff(y(x),x) = (-128*x*y(x)-24*x^3+32*x^2-128*x+512*y(x)^3+192*x^2*y(x)^2-384*x*y(x)^2+24*y(x)*x^4-96*x^3*y(x)+96*x^2*y(x)+x^6-6*x^5+12*x^4)/(512*y(x)+64*x^2-128*x+512),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{8}+\frac {x}{4}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {4 \textit {\_a} +4}{4 \textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.36 (sec). Leaf size: 53
DSolve[y'[x] == (-128*x + 32*x^2 - 24*x^3 + 12*x^4 - 6*x^5 + x^6 - 128*x*y[x] + 96*x^2*y[x] - 96*x^3*y[x] + 24*x^4*y[x] - 384*x*y[x]^2 + 192*x^2*y[x]^2 + 512*y[x]^3)/(512 - 128*x + 64*x^2 + 512*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x-16 \text {RootSum}\left [6656 \text {$\#$1}^3-23 \text {$\#$1}-1\&,\text {$\#$1} \log \left (79872 \text {$\#$1}^2-18304 \text {$\#$1}+181 x^2+1448 y(x)-362 x-184\right )\&\right ]=c_1,y(x)\right ] \]