84.10.4 problem 5.14

Internal problem ID [22132]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 5. Homogeneous differential equations. Supplementary problems
Problem number : 5.14
Date solved : Thursday, October 02, 2025 at 08:28:59 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {x \left (c_1 x -4\right )} \\ y &= -\sqrt {x \left (c_1 x -4\right )} \\ \end{align*}

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.269 (sec). Leaf size: 26

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

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