Internal problem ID [32]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y^{\prime }-3 \sqrt {y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
dsolve(diff(y(x),x) = 3*(x*y(x))^(1/2),y(x), singsol=all)
\[ \frac {x^{2}}{\left (-x^{3}+y \relax (x )\right ) \left (-x^{2}+\sqrt {x y \relax (x )}\right )}+\frac {\sqrt {x y \relax (x )}}{\left (-x^{3}+y \relax (x )\right ) \left (-x^{2}+\sqrt {x y \relax (x )}\right )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 26
DSolve[y'[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*}