73.5.15 problem 6.7 (c)

Internal problem ID [15126]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (c)
Date solved : Tuesday, January 28, 2025 at 07:34:14 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 26

DSolve[3*D[y[x],x]+2/x*y[x]==4*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (x^{4/3}+2 c_1\right ){}^2}{4 x^{2/3}} \]