4.2.37 problem 38

Internal problem ID [1165]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 38
Date solved : Tuesday, September 30, 2025 at 04:25:33 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

\begin{align*} y &= \sqrt {c_1 x +1}\, x \\ y &= -\sqrt {c_1 x +1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to -x \sqrt {1+c_1 x}\\ y(x)&\to x \sqrt {1+c_1 x} \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 26

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)
 

\[ \left [ y{\left (x \right )} = - x \sqrt {C_{1} x + 1}, \ y{\left (x \right )} = x \sqrt {C_{1} x + 1}\right ] \]