23.1.331 problem 317

Internal problem ID [4938]
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 : 317
Date solved : Tuesday, September 30, 2025 at 09:03:25 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 84

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

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

✓ Sympy. Time used: 0.328 (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) + (2*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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