29.12.15 problem 334

Internal problem ID [4934]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 334
Date solved : Monday, January 27, 2025 at 09:52:38 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 45

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

\[ y \left (x \right ) = \frac {2 \sqrt {x \left (x -1\right )}-\ln \left (2\right )+\ln \left (2 x -1+2 \sqrt {x \left (x -1\right )}\right )+4 c_{1}}{4 \sqrt {x \left (x -1\right )}} \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 71

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

\[ y(x)\to \frac {-2 \sqrt {x-1} \sqrt {x} \text {arctanh}\left (\frac {\sqrt {x-1}}{\sqrt {x}+1}\right )-x^2+2 c_1 \sqrt {x-x^2}+x}{2 x-2 x^2} \]