23.1.332 problem 318

Internal problem ID [4939]
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 : 318
Date solved : Tuesday, September 30, 2025 at 09:03:27 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \frac {12 c_1 \,x^{4}+4 a x -3 a}{12 \left (-1+x \right )^{2}} \]

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 84

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

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

✓ Sympy. Time used: 0.358 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {C_{1} x^{4} + \frac {a x}{3} - \frac {a}{4}}{x^{2} - 2 x + 1} \]