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 : Monday, January 27, 2025 at 02:38:03 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 66

dsolve(diff(y(x),x)=sqrt(x*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==Sqrt[x*y[x]],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*}