Internal problem ID [2821]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 66.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-x -\left (1-2 x \right ) y+\left (1-x \right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 23
dsolve(diff(y(x),x) = x+(1-2*x)*y(x)-(1-x)*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {2 \,{\mathrm e}^{-x}}{c_{1}-2 x \,{\mathrm e}^{-x}} \]
✓ Solution by Mathematica
Time used: 0.171 (sec). Leaf size: 22
DSolve[y'[x]==x+(1-2 x)y[x]-(1-x)y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {1}{x+c_1 e^x} \\ y(x)\to 1 \\ \end{align*}