Internal problem ID [8495]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 915.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {-y^{3}-y+4 y^{2} \ln \relax (x )-4 \ln \relax (x )^{2} y^{3}-1+6 y \ln \relax (x )-12 \ln \relax (x )^{2} y^{2}+8 \ln \relax (x )^{3} y^{3}}{y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 43
dsolve(diff(y(x),x) = -(-y(x)^3-y(x)+4*y(x)^2*ln(x)-4*ln(x)^2*y(x)^3-1+6*y(x)*ln(x)-12*ln(x)^2*y(x)^2+8*ln(x)^3*y(x)^3)/y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {9}{18 \ln \relax (x )+83 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{6889 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \relax (x )+3 c_{1}\right )-3} \]
✓ Solution by Mathematica
Time used: 0.605 (sec). Leaf size: 724
DSolve[y'[x] == (1 + y[x] - 6*Log[x]*y[x] - 4*Log[x]*y[x]^2 + 12*Log[x]^2*y[x]^2 + y[x]^3 + 4*Log[x]^2*y[x]^3 - 8*Log[x]^3*y[x]^3)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (4 \text {RootSum}\left [8 \text {$\#$1}^3 K[1]^3-4 \text {$\#$1}^2 K[1]^3-3 K[1]^3-12 \text {$\#$1}^2 K[1]^2+4 \text {$\#$1} K[1]^2+6 \text {$\#$1} K[1]-K[1]-1\&,\frac {\log (\log (x)-\text {$\#$1})}{12 \text {$\#$1}^2 K[1]^2-4 \text {$\#$1} K[1]^2-12 \text {$\#$1} K[1]+2 K[1]+3}\&\right ] K[1]-\frac {2 K[1]}{8 \log ^3(x) K[1]^3-4 \log ^2(x) K[1]^3-3 K[1]^3-12 \log ^2(x) K[1]^2+4 \log (x) K[1]^2+6 \log (x) K[1]-K[1]-1}-\frac {2 \text {RootSum}\left [8 \text {$\#$1}^3 K[1]^3-4 \text {$\#$1}^2 K[1]^3-3 K[1]^3-12 \text {$\#$1}^2 K[1]^2+4 \text {$\#$1} K[1]^2+6 \text {$\#$1} K[1]-K[1]-1\&,\frac {16 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3-224 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3-36 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^3-6 \log (\log (x)-\text {$\#$1}) K[1]^3+216 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3+36 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3-8 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^2-4 \text {$\#$1}^2 K[1]^2-108 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^2-16 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2+116 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2-54 \text {$\#$1} K[1]^2+9 K[1]^2+4 \log (x) \log (\log (x)-\text {$\#$1}) K[1]-2 \log (\log (x)-\text {$\#$1}) K[1]+8 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]+4 \text {$\#$1} K[1]+27 K[1]-2 \log (\log (x)-\text {$\#$1})-1}{8 \log (x) \text {$\#$1}^2 K[1]^3-112 \text {$\#$1}^2 K[1]^3+492 \log (x) K[1]^3+108 \log (x) \text {$\#$1} K[1]^3-492 \text {$\#$1} K[1]^3-3 K[1]^3-4 \text {$\#$1}^2 K[1]^2-54 \log (x) K[1]^2-8 \log (x) \text {$\#$1} K[1]^2+58 \text {$\#$1} K[1]^2+2 \log (x) K[1]+4 \text {$\#$1} K[1]-K[1]-1}\&\right ]}{K[1]}\right )dK[1]-2 \left (y(x)^2 \text {RootSum}\left [8 \text {$\#$1}^3 y(x)^3-4 \text {$\#$1}^2 y(x)^3-12 \text {$\#$1}^2 y(x)^2+4 \text {$\#$1} y(x)^2+6 \text {$\#$1} y(x)-3 y(x)^3-y(x)-1\&,\frac {\log (\log (x)-\text {$\#$1})}{12 \text {$\#$1}^2 y(x)^2-4 \text {$\#$1} y(x)^2-12 \text {$\#$1} y(x)+2 y(x)+3}\&\right ]+\log (x)\right )=c_1,y(x)\right ] \]