Internal problem ID [3553]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 297.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+\left (2 x -y\right ) y=1} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.213 (sec). Leaf size: 52
DSolve[(1-x^2)y'[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*}