29.30.36 problem 896

Internal problem ID [5476]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 896
Date solved : Monday, January 27, 2025 at 11:25:30 AM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-x y^{\prime }+y \left (1-y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.045 (sec). Leaf size: 31

DSolve[x^2 (D[y[x],x])^2-x D[y[x],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*}