60.2.163 problem 739

Internal problem ID [10750]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 739
Date solved : Monday, January 27, 2025 at 09:39:57 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 39

dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x*y(x)+2*x*y(x)^2),y(x), singsol=all)
 

\begin{align*} y &= -{\frac {1}{2}} \\ y &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+4\right )}}{2}-\frac {1}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 46

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{4 (2 K[1]+1)}-\frac {1}{4}\right )dK[1]-\frac {1}{2 x (2 y(x)+1)}=c_1,y(x)\right ] \]