Internal problem ID [3060]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 312.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime }-2 y x +2=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {2 x -2 \ln \relax (x )+c_{1}}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 21
DSolve[x(1-x)y'[x]==2(x y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x-2 \log (x)+c_1}{(x-1)^2} \\ \end{align*}