Internal problem ID [3624]
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]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-y^{\prime } x +y \left (1-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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 \relax (x ) = c_{1} x \\ y \relax (x ) = \frac {c_{1}+x}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.041 (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*}