Internal problem ID [101]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {6 y+y^{\prime } x -3 x y^{\frac {4}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(6*y(x)+x*diff(y(x),x) = 3*x*y(x)^(4/3),y(x), singsol=all)
\[ \frac {1}{y \relax (x )^{\frac {1}{3}}}-x -c_{1} x^{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 22
DSolve[6*y[x]+x*y'[x] == 3*x*y[x]^(4/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^3 (1+c_1 x){}^3} \\ y(x)\to 0 \\ \end{align*}