41.1.17 problem 17

Internal problem ID [8684]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 05:41:04 PM
CAS classification : [_separable]

\begin{align*} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=1/x^(1/2)+diff(y(x),x)/y(x)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 21

ode=1/Sqrt[x]+D[y[x],x]/Sqrt[y[x]]==0; 
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 \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 15

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

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