8.3.6 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 : Monday, January 27, 2025 at 02:57:40 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 65

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

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

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 26

DSolve[D[y[x],x] == 3*(x*y[x])^(1/2),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*}