Internal problem ID [4132]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 896.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} {y^{\prime }}^{2}-x y^{\prime }+y \left (1-y\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2-x*diff(y(x),x)+y(x)*(1-y(x)) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x y \left (x \right ) = \frac {x +c_{1}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 31
DSolve[x^2 (y'[x])^2-x y'[x]+y[x](1-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x y(x)\to \frac {x+c_1}{x} y(x)\to 0 y(x)\to 1 \end{align*}