85.11.1 problem 2

Internal problem ID [22493]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 37
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:42:09 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

\begin{align*} y &= -\frac {\sqrt {-x^{2}+4 c_1}\, x}{2} \\ y &= \frac {\sqrt {-x^{2}+4 c_1}\, x}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.319 (sec). Leaf size: 51

ode=D[y[x],x]== (4*y[x]^2-x^4)/(4*x*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} \sqrt {-x^4+4 c_1 x^2}\\ y(x)&\to \frac {1}{2} \sqrt {-x^4+4 c_1 x^2} \end{align*}

✓ Sympy. Time used: 0.247 (sec). Leaf size: 29

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

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