38.1.17 problem 19

Internal problem ID [8178]
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. Exercises 1.1 at page 12
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 05:18:15 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 20

ode=D[y[x],x]==2*x*y[x]^2; 
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: 0.077 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

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