40.3.21 problem 25 (f)

Internal problem ID [6625]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (f)
Date solved : Sunday, March 30, 2025 at 11:12:45 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {\left (3 x +c_1 \right ) x} \\ y &= -\sqrt {\left (3 x +c_1 \right ) x} \\ \end{align*}

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 42

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

✓ Sympy. Time used: 0.425 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - \sqrt {x \left (C_{1} + 3 x\right )}, \ y{\left (x \right )} = \sqrt {x \left (C_{1} + 3 x\right )}\right ] \]