23.1.349 problem 335

Internal problem ID [4956]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 335
Date solved : Tuesday, September 30, 2025 at 09:05:38 AM
CAS classification : [_linear]

\begin{align*} x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=x*(1-2*x)*diff(y(x),x)+1+(1-4*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 88

ode=x*(1-2*x)*D[y[x],x]+1+(1-4*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {1-4 K[1]}{K[1]-2 K[1]^2}dK[1]\right ) \left (\int _1^x-\frac {\exp \left (-\int _1^{K[2]}-\frac {1-4 K[1]}{K[1]-2 K[1]^2}dK[1]\right )}{K[2]-2 K[2]^2}dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - 2*x)*Derivative(y(x), x) + (1 - 4*x)*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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