Internal problem ID [8519]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 939.
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 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 y x^{4}-48 y x^{3}-48 y x^{2}+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve(diff(y(x),x) = (-32*x*y(x)+16*x^3+16*x^2-32*x-64*y(x)^3+48*x^2*y(x)^2+96*x*y(x)^2-12*y(x)*x^4-48*x^3*y(x)-48*x^2*y(x)+x^6+6*x^5+12*x^4)/(-64*y(x)+16*x^2+32*x-64),y(x), singsol=all)
\[ x -\frac {4 \ln \left (y \relax (x )-\frac {x^{2}}{4}-\frac {x}{2}-1\right )}{5}+\frac {2 \ln \left (2 \left (y \relax (x )-\frac {x^{2}}{4}-\frac {x}{2}\right )^{2}+2 y \relax (x )-\frac {x^{2}}{2}-x +1\right )}{5}-\frac {2 \arctan \left (-2 y \relax (x )+\frac {x^{2}}{2}+x -1\right )}{5}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.361 (sec). Leaf size: 136
DSolve[y'[x] == (-32*x + 16*x^2 + 16*x^3 + 12*x^4 + 6*x^5 + x^6 - 32*x*y[x] - 48*x^2*y[x] - 48*x^3*y[x] - 12*x^4*y[x] + 96*x*y[x]^2 + 48*x^2*y[x]^2 - 64*y[x]^3)/(-64 + 32*x + 16*x^2 - 64*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{5} \text {RootSum}\left [\text {$\#$1}^4+4 \text {$\#$1}^3-8 \text {$\#$1}^2 y(x)-16 \text {$\#$1} y(x)-8 \text {$\#$1}+16 y(x)^2+16 y(x)+8\&,\frac {\text {$\#$1}^2 (-\log (x-\text {$\#$1}))+4 y(x) \log (x-\text {$\#$1})-2 \text {$\#$1} \log (x-\text {$\#$1})+3 \log (x-\text {$\#$1})}{-\text {$\#$1}^2-2 \text {$\#$1}+4 y(x)+2}\&\right ]-\frac {4}{5} \log \left (x^2-4 y(x)+2 x+4\right )+x=c_1,y(x)\right ] \]