29.14.24 problem 405

Internal problem ID [5003]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 405
Date solved : Tuesday, March 04, 2025 at 07:42:13 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \sqrt {X}+\sqrt {Y}&=0 \end{align*}

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

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

\[ y \left (x \right ) = -\frac {\sqrt {Y}\, x}{\sqrt {X}}+c_{1} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

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

\[ y(x)\to -\frac {x \sqrt {Y}}{\sqrt {X}}+c_1 \]

✓ Sympy. Time used: 0.137 (sec). Leaf size: 15

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

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