29.13.10 problem 364

Internal problem ID [4964]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 364
Date solved : Monday, January 27, 2025 at 09:58:24 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(x^2*(1-x)*diff(y(x),x) = (2-x)*x*y(x)-y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{2}}{1+c_{1} \left (x -1\right )} \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 25

DSolve[x^2(1-x)D[y[x],x]==(2-x)x y[x]-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{c_1 (-x)+1+c_1} \\ y(x)\to 0 \\ \end{align*}