23.1.253 problem 247

Internal problem ID [4860]
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 : 247
Date solved : Tuesday, September 30, 2025 at 08:45:26 AM
CAS classification : [_linear]

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

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

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

\[ y = \frac {x^{2}}{\sqrt {1-x}}+\frac {c_1}{\sqrt {-1+x}} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \frac {2 x^2+\sqrt {2} c_1}{2 \sqrt {1-x}} \end{align*}

✓ Sympy. Time used: 2.239 (sec). Leaf size: 36

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

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