8.6.22 problem 22

Internal problem ID [792]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 22
Date solved : Wednesday, February 05, 2025 at 04:21:00 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }&=12 x^{4} y^{{2}/{3}}+6 y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x*diff(y(x),x) = 12*x^4*y(x)^(2/3)+6*y(x),y(x), singsol=all)
 

\[ -2 x^{4}-c_1 \,x^{2}+y^{{1}/{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 19

DSolve[x*D[y[x],x]== 12*x^4*y[x]^(2/3)+6*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^6 \left (2 x^2+c_1\right ){}^3 \]