10.2.36 problem 37

Internal problem ID [1164]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 37
Date solved : Saturday, March 29, 2025 at 10:43:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

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

\begin{align*} y &= -\frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_1 \right )}}{5 x^{2}} \\ y &= \frac {\sqrt {5}\, \sqrt {x \left (x^{5}+5 c_1 \right )}}{5 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.206 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^5}{5}+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {\frac {x^5}{5}+c_1}}{x^{3/2}} \\ \end{align*}

✓ Sympy. Time used: 0.473 (sec). Leaf size: 42

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

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