Internal problem ID [9219]
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]
\[ \boxed {y^{\prime }+\frac {\left (-1-y^{4}+2 y^{2} x^{2}-x^{4}-y^{6}+3 y^{4} x^{2}-3 y^{2} x^{4}+x^{6}\right ) x}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 105
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)
\[ y \left (x \right ) = -{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}} x^{2}-2 x^{3} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right )+2 \,{\mathrm e}^{2 \textit {\_Z}} c_{1} +\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right ) x -4 x c_{1} {\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+1\right )}+x \]
✓ Solution by Mathematica
Time used: 0.475 (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]
\[ \text {Solve}\left [\frac {1}{4} \left (2 \log \left (-x^2+y(x)^2+1\right )-2 x^2-\frac {1}{y(x) (y(x)+x)}+\frac {1}{x y(x)-y(x)^2}-2 \log (x-y(x))-2 \log (y(x)+x)\right )=c_1,y(x)\right ] \]