Internal problem ID [8509]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 929.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+y^{3} x^{3}}{32 y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x) = -1/32/y(x)*(16*x*y(x)^3-8*y(x)^3-8*y(x)+8*x*y(x)^2-2*x^2*y(x)^3-8+12*x*y(x)-6*x^2*y(x)^2+x^3*y(x)^3)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {18}{58 \RootOf \left (-324 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \relax (x )+12 c_{1}\right )+9 x -6} \]
✓ Solution by Mathematica
Time used: 0.524 (sec). Leaf size: 683
DSolve[y'[x] == (1/4 + y[x]/4 - (3*x*y[x])/8 - (x*y[x]^2)/4 + (3*x^2*y[x]^2)/16 + y[x]^3/4 - (x*y[x]^3)/2 + (x^2*y[x]^3)/16 - (x^3*y[x]^3)/32)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (-32 \text {RootSum}\left [\text {$\#$1}^3 K[1]^3-2 \text {$\#$1}^2 K[1]^3-8 K[1]^3-6 \text {$\#$1}^2 K[1]^2+8 \text {$\#$1} K[1]^2+12 \text {$\#$1} K[1]-8 K[1]-8\&,\frac {\log (x-\text {$\#$1})}{3 \text {$\#$1}^2 K[1]^2-4 \text {$\#$1} K[1]^2-12 \text {$\#$1} K[1]+8 K[1]+12}\&\right ] K[1]+\frac {32 K[1]}{x^3 K[1]^3-2 x^2 K[1]^3-8 K[1]^3-6 x^2 K[1]^2+8 x K[1]^2+12 x K[1]-8 K[1]-8}-\frac {8 \text {RootSum}\left [\text {$\#$1}^3 K[1]^3-2 \text {$\#$1}^2 K[1]^3-8 K[1]^3-6 \text {$\#$1}^2 K[1]^2+8 \text {$\#$1} K[1]^2+12 \text {$\#$1} K[1]-8 K[1]-8\&,\frac {-x \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+20 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+12 x \log (x-\text {$\#$1}) K[1]^3+8 \log (x-\text {$\#$1}) K[1]^3-18 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^3-12 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^3+2 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^2+\text {$\#$1}^2 K[1]^2+36 x \log (x-\text {$\#$1}) K[1]^2+4 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^2-44 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^2+18 \text {$\#$1} K[1]^2-12 K[1]^2-4 x \log (x-\text {$\#$1}) K[1]+8 \log (x-\text {$\#$1}) K[1]-8 \log (x-\text {$\#$1}) \text {$\#$1} K[1]-4 \text {$\#$1} K[1]-36 K[1]+8 \log (x-\text {$\#$1})+4}{x \text {$\#$1}^2 K[1]^3-20 \text {$\#$1}^2 K[1]^3+112 x K[1]^3+18 x \text {$\#$1} K[1]^3-112 \text {$\#$1} K[1]^3-8 K[1]^3-2 \text {$\#$1}^2 K[1]^2-36 x K[1]^2-4 x \text {$\#$1} K[1]^2+44 \text {$\#$1} K[1]^2+4 x K[1]+8 \text {$\#$1} K[1]-8 K[1]-8}\&\right ]}{K[1]}\right )dK[1]+16 y(x)^2 \text {RootSum}\left [\text {$\#$1}^3 y(x)^3-2 \text {$\#$1}^2 y(x)^3-6 \text {$\#$1}^2 y(x)^2+8 \text {$\#$1} y(x)^2+12 \text {$\#$1} y(x)-8 y(x)^3-8 y(x)-8\&,\frac {\log (x-\text {$\#$1})}{3 \text {$\#$1}^2 y(x)^2-4 \text {$\#$1} y(x)^2-12 \text {$\#$1} y(x)+8 y(x)+12}\&\right ]+\log (x)=c_1,y(x)\right ] \]