44.5.6 problem 6

Internal problem ID [7068]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 6
Date solved : Sunday, March 30, 2025 at 11:37:28 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = \frac {1}{x^{2}+c_1} \]

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 20

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

\begin{align*} y(x)\to \frac {1}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {1}{C_{1} + x^{2}} \]