29.3.12 problem 66

Internal problem ID [4674]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 66
Date solved : Monday, January 27, 2025 at 09:31:03 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 30

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

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