89.2.5 problem 5

Internal problem ID [24270]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 27
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:04:02 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}+2 y^{2}-x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=x^2+2*y(x)^2-x*y(x)*diff(y(x),x) = 0; 
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: 0.313 (sec). Leaf size: 38

ode=(x^2+2*y[x]^2)-(x*y[x])*D[y[x],x]==0; 
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: 0.234 (sec). Leaf size: 29

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

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