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 : Sunday, March 30, 2025 at 04:16:15 AM
CAS classification : [_linear]

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

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

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

\[ y = \frac {2 \sqrt {x \left (-1+x \right )}-\ln \left (2\right )+\ln \left (-1+2 x +2 \sqrt {x \left (-1+x \right )}\right )+4 c_1}{4 \sqrt {x \left (-1+x \right )}} \]

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

ode=2 x(1-x)D[y[x],x]+x+(1-2 x)y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 2.354 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(1 - x)*Derivative(y(x), x) + x + (1 - 2*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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