73.5.15 problem 6.7 (c)

Internal problem ID [15055]
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 : Monday, March 31, 2025 at 01:17:16 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

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

ode:=3*diff(y(x),x)+2*y(x)/x = 4*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=3*D[y[x],x]+2/x*y[x]==4*Sqrt[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.283 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*sqrt(y(x)) + 3*Derivative(y(x), x) + 2*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{x^{\frac {2}{3}}} + C_{1} x^{\frac {2}{3}} + \frac {x^{2}}{4} \]