23.1.327 problem 313

Internal problem ID [4934]
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 : 313
Date solved : Tuesday, September 30, 2025 at 09:03:19 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.174 (sec). Leaf size: 82

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

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

✓ Sympy. Time used: 0.225 (sec). Leaf size: 22

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

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