Internal problem ID [3439]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 701.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 46
dsolve(x*(2-x*y(x)^2-2*x*y(x)^3)*diff(y(x),x)+1+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -{\frac {1}{2}} \\ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (x \,{\mathrm e}^{3 \textit {\_Z}}-4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x +3 \,{\mathrm e}^{\textit {\_Z}} x +16\right )}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.328 (sec). Leaf size: 47
DSolve[x(2-x y[x]^2-2 x y[x]^3)y'[x]+1+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ] \]