83.10.14 problem 14

Internal problem ID [21983]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 14
Date solved : Thursday, October 02, 2025 at 08:21:23 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\begin{align*} y &= \frac {c_1}{x} \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to c_1\\ y(x)&\to \frac {c_1}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 8

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

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