44.2.18 problem 18

Internal problem ID [6950]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 18
Date solved : Sunday, March 30, 2025 at 11:30:39 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 66

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

\[ \frac {3 \left (c_1 \,x^{3}-9 y c_1 +1\right ) \sqrt {x y}-x^{2} \left (c_1 \,x^{3}-9 y c_1 -1\right )}{\left (x^{3}-9 y\right ) \left (x^{2}-3 \sqrt {x y}\right )} = 0 \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 28

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

\begin{align*} y(x)\to \frac {1}{36} \left (2 x^{3/2}+3 c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.556 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} - \frac {C_{1} \sqrt {x^{3}}}{3} + \frac {x^{3}}{9} \]