Internal problem ID [3082]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 334.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 35
dsolve(2*x*(1-x)*diff(y(x),x)+x+(1-2*x)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}+\frac {\ln \left (-\frac {1}{2}+x +\sqrt {x \left (x -1\right )}\right )}{4 \sqrt {x \left (x -1\right )}}+\frac {c_{1}}{\sqrt {x \left (x -1\right )}} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 50
DSolve[2 x(1-x)y'[x]+x+(1-2 x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\frac {\tanh ^{-1}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )}{\sqrt {x-1} \sqrt {x}}+\frac {2 c_1}{\sqrt {-((x-1) x)}}+1\right ) \\ \end{align*}