29.11.25 problem 316

Internal problem ID [4916]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 316
Date solved : Monday, January 27, 2025 at 09:50:30 AM
CAS classification : [_linear]

\begin{align*} x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(x*(1-x)*diff(y(x),x)+2-3*x*y(x)+y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

DSolve[x(1-x)D[y[x],x]+(2-3 x y[x]+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2-2 x+c_1}{(x-1)^2 x} \]