32.6.42 problem Exercise 12.42, page 103

Internal problem ID [5907]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.42, page 103
Date solved : Sunday, March 30, 2025 at 10:25:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {\left (-3 x +c_1 \right ) x} \\ y &= -\sqrt {c_1 x -3 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.395 (sec). Leaf size: 35

ode=2*x*y[x]*D[y[x],x]+3*x^2-y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {x (-3 x+c_1)} \\ y(x)\to \sqrt {x (-3 x+c_1)} \\ \end{align*}

✓ Sympy. Time used: 0.420 (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)
 

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