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 : Friday, February 07, 2025 at 08:12:56 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=3*sqrt(x*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==3*Sqrt[x*y[x]],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*}