29.11.6 problem 297

Internal problem ID [4897]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 297
Date solved : Monday, January 27, 2025 at 09:46:52 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 52

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

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