76.19.3 problem Ex. 3

Internal problem ID [20135]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 3
Date solved : Thursday, October 02, 2025 at 05:32:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 16

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

\[ \sqrt {y}-\sqrt {x}-c_1 = 0 \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {1}{4} \left (2 \sqrt {x}+c_1\right ){}^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 15

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

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