23.1.197 problem 195

Internal problem ID [4804]
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 : 195
Date solved : Tuesday, September 30, 2025 at 08:41:15 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=4 y-4 \sqrt {y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ -c_1 \,x^{2}+\sqrt {y}-1 = 0 \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \left (1+e^{\frac {c_1}{2}} x^2\right ){}^2\\ y(x)&\to 0\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.246 (sec). Leaf size: 20

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

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