83.4.20 problem 20

Internal problem ID [19013]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 20
Date solved : Thursday, March 13, 2025 at 01:22:21 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 26

ode:=x^2+3*y(x)^2-2*x*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x -1}\, x \\ y \left (x \right ) &= -\sqrt {c_{1} x -1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.286 (sec). Leaf size: 34

ode=(x^2+3*y[x]^2)-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} \\ y(x)\to x \sqrt {-1+c_1 x} \\ \end{align*}

✓ Sympy. Time used: 0.371 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 - 2*x*y(x)*Derivative(y(x), x) + 3*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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