7.3.6 problem 6

Internal problem ID [46]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 6
Date solved : Tuesday, March 04, 2025 at 10:40:15 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=3 \sqrt {x y} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 65

ode:=diff(y(x),x) = 3*(x*y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (c_1 \,x^{3}-y c_1 +1\right ) \sqrt {y x}-x^{2} \left (c_1 \,x^{3}-y c_1 -1\right )}{\left (x^{3}-y\right ) \left (x^{2}-\sqrt {y x}\right )} = 0 \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 26

ode=D[y[x],x]==3*Sqrt[x*y[x]]; 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (2 x^{3/2}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.461 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*sqrt(x*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} - C_{1} \sqrt {x^{3}} + x^{3} \]