7.7.22 problem 22

Internal problem ID [200]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 22
Date solved : Friday, February 07, 2025 at 08:07:14 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 19

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

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