Internal problem ID [8464]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 884.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (-1-y^{4}+2 x^{2} y^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 x^{4} y^{2}+x^{6}\right ) x}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 107
dsolve(diff(y(x),x) = -(-1-y(x)^4+2*x^2*y(x)^2-x^4-y(x)^6+3*x^2*y(x)^4-3*x^4*y(x)^2+x^6)*x/y(x),y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{\RootOf \left (3 \,{\mathrm e}^{2 \textit {\_Z}} x^{2}-6 \,{\mathrm e}^{\textit {\_Z}} x^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right )-2 \,{\mathrm e}^{2 \textit {\_Z}} c_{1}+3 \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} +6 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right ) x +4 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x +3\right )}+x \]
✓ Solution by Mathematica
Time used: 0.539 (sec). Leaf size: 71
DSolve[y'[x] == (x*(1 + x^4 - x^6 - 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 - 3*x^2*y[x]^4 + y[x]^6))/y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{4} \left (2 \log \left (-x^2+y(x)^2+1\right )-2 x^2-\frac {1}{y(x) (y(x)+x)}+\frac {1}{x y(x)-y(x)^2}-2 \log (x-y(x))-2 \log (y(x)+x)\right )=c_1,y(x)\right ] \]