88.12.25 problem 27

Internal problem ID [24081]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:57:32 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 34

ode=(3*y[x]^2-2*x^2)==2*x*y[x]*D[y[x],{x,1}]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.232 (sec). Leaf size: 26

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

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