81.1.10 problem 2-8

Internal problem ID [21455]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-8
Date solved : Thursday, October 02, 2025 at 07:38:29 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

ode=Sqrt[x]*D[y[x],x]+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.125 (sec). Leaf size: 10

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

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