Internal problem ID [129]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y+y^{\prime } x -6 x^{2} \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(2*y(x)+x*diff(y(x),x) = 6*x^2*y(x)^(1/2),y(x), singsol=all)
\[ -x^{2}-\frac {c_{1}}{x}+\sqrt {y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 17
DSolve[2*y[x]+x*y'[x] == 6*x^2*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x^3+c_1\right ){}^2}{x^2} \\ \end{align*}