Internal problem ID [8521]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 941.
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 {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 y x^{4}-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x) = (-32*x*y(x)-72*x^3+32*x^2-32*x+64*y(x)^3+48*x^2*y(x)^2-192*x*y(x)^2+12*y(x)*x^4-96*x^3*y(x)+192*x^2*y(x)+x^6-12*x^5+48*x^4)/(64*y(x)+16*x^2-64*x+64),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{4}+x +\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.334 (sec). Leaf size: 53
DSolve[y'[x] == (-32*x + 32*x^2 - 72*x^3 + 48*x^4 - 12*x^5 + x^6 - 32*x*y[x] + 192*x^2*y[x] - 96*x^3*y[x] + 12*x^4*y[x] - 192*x*y[x]^2 + 48*x^2*y[x]^2 + 64*y[x]^3)/(64 - 64*x + 16*x^2 + 64*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x-8 \text {RootSum}\left [11776 \text {$\#$1}^3-40 \text {$\#$1}-1\&,\text {$\#$1} \log \left (17664 \text {$\#$1}^2-1472 \text {$\#$1}+11 x^2+44 y(x)-44 x-40\right )\&\right ]=c_1,y(x)\right ] \]