35.4.2 problem 2

Internal problem ID [6120]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 2
Date solved : Sunday, March 30, 2025 at 10:39:15 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ \sqrt {y}-\frac {x^{3}+3 c_1}{3 \sqrt {x}} = 0 \]

✓ Mathematica. Time used: 0.184 (sec). Leaf size: 22

ode=D[y[x],x]+1/x*y[x]==2*x^(3/2)*y[x]^(1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (x^3+3 c_1\right ){}^2}{9 x} \]

✓ Sympy. Time used: 0.270 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{x} + \frac {2 C_{1} x^{2}}{3} + \frac {x^{5}}{9} \]