83.8.1 problem 1

Internal problem ID [21954]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. IX at page 55
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:19:38 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} x y \left (x y^{\prime }+y\right )&=4 x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 34

ode:=x*y(x)*(x*diff(y(x),x)+y(x)) = 4*x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 42

ode=x*y[x]*(x*D[y[x],x]+y[x])==4*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.235 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3 + x*(x*Derivative(y(x), x) + y(x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 2 x^{4}}}{x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 2 x^{4}}}{x}\right ] \]