13.10 problem 364

Internal problem ID [3112]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 13
Problem number: 364.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

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

Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 25

DSolve[x^2(1-x)y'[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*}