8.5.23 problem 23

Internal problem ID [751]
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
Date solved : Monday, January 27, 2025 at 03:02:41 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 22

DSolve[6*y[x]+x*D[y[x],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*}