29.4.17 problem 106

Internal problem ID [4708]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 106
Date solved : Tuesday, March 04, 2025 at 07:08:39 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.123 (sec). Leaf size: 12

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

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