Internal problem ID [3314]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 572.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 34
dsolve(x^2*(1-y(x))*diff(y(x),x)+(1+x)*y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (-\frac {{\mathrm e}^{-c_{1}+\frac {1}{x}}}{x}\right ) x +\ln \relax (x ) x +c_{1} x -1}{x}} \]
✓ Solution by Mathematica
Time used: 0.207 (sec). Leaf size: 25
DSolve[x^2(1-y[x])y'[x]+(1+x)y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\text {ProductLog}\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} \\ \end{align*}