84.10.3 problem 5.13

Internal problem ID [22131]
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 : 5.13
Date solved : Thursday, October 02, 2025 at 08:28:48 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}-1}\, x \\ y &= -\sqrt {c_1 \,x^{2}-1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.342 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.238 (sec). Leaf size: 29

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

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