2.3.6 problem 6

Internal problem ID [682]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 04:05:46 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 65

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

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

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 26

ode=D[y[x],x] == 3*(x*y[x])^(1/2); 
ic={}; 
DSolve[{ode,ic},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: 0.277 (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)
 

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