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]
\[ \boxed {2 y+y^{\prime } x -6 x^{2} \sqrt {y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(2*y(x)+x*diff(y(x),x) = 6*x^2*y(x)^(1/2),y(x), singsol=all)
\[ \frac {-x^{3}+\sqrt {y \left (x \right )}\, x -c_{1}}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 17
DSolve[2*y[x]+x*y'[x] == 6*x^2*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (x^3+c_1\right ){}^2}{x^2} \]