Internal problem ID [142]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x -12 x^{4} y^{\frac {2}{3}}-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x) = 12*x^4*y(x)^(2/3)+6*y(x),y(x), singsol=all)
\[ -2 x^{4}-c_{1} x^{2}+y \relax (x )^{\frac {1}{3}} = 0 \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 19
DSolve[x*y'[x]== 12*x^4*y[x]^(2/3)+6*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^6 \left (2 x^2+c_1\right ){}^3 \\ \end{align*}