29.11.21 problem 312

Internal problem ID [4912]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 312
Date solved : Monday, January 27, 2025 at 09:50:23 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 21

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

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