29.25.4 problem 701

Internal problem ID [5291]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 701
Date solved : Monday, January 27, 2025 at 11:04:38 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (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 \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {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: 0.311 (sec). Leaf size: 47

DSolve[x(2-x y[x]^2-2 x y[x]^3)D[y[x],x]+1+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ] \]