83.1.6 problem 4

Internal problem ID [21911]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter II. Definitions and fundamentals
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:09:17 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to -\frac {1}{2} \sqrt {-x^2+8 c_1}\\ y(x)&\to \frac {1}{2} \sqrt {-x^2+8 c_1} \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 26

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

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