44.2.6 problem 6

Internal problem ID [6938]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 6
Date solved : Sunday, March 30, 2025 at 11:29:46 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=-4 \end{align*}

✓ Maple. Time used: 0.151 (sec). Leaf size: 15

ode:=diff(y(x),x)+2*x*y(x)^2 = 0; 
ic:=y(1/2) = -4; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 16

ode=D[y[x],x]+2*x*y[x]^2==0; 
ic={y[1/2]==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2}{2 x^2-1} \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**2 + Derivative(y(x), x),0) 
ics = {y(1/2): -4} 
dsolve(ode,func=y(x),ics=ics)
 

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