29.12.14 problem 333

Internal problem ID [4933]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 333
Date solved : Monday, January 27, 2025 at 09:52:35 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} x \left (1-2 x \right ) y^{\prime }&=4 x -\left (1+4 x \right ) y+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(x*(1-2*x)*diff(y(x),x) = 4*x-(1+4*x)*y(x)+y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-2 x^{2}+c_{1}}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 27

DSolve[x(1-2 x)D[y[x],x]==4 x -(1+4 x)y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+\frac {x (2 x-1)}{x-c_1} \\ y(x)\to 1 \\ \end{align*}