7.7.24 problem 24

Internal problem ID [202]
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 : 24
Date solved : Tuesday, March 04, 2025 at 11:02:16 AM
CAS classification : [_separable]

\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

ode:=9*x^2*y(x)^2+x^(3/2)*diff(y(x),x) = y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {x}}{2+6 x^{2}+c_1 \sqrt {x}} \]

✓ Mathematica. Time used: 0.181 (sec). Leaf size: 34

ode=9*x^2*y[x]^2+x^(3/2)*D[y[x],x]==y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {\sqrt {x}}{6 x^2-c_1 \sqrt {x}+2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**(3/2)*Derivative(y(x), x) + 9*x**2*y(x)**2 - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {x}}{C_{1} \sqrt {x} + 6 x^{2} + 2} \]