1.2.9 problem 11

Internal problem ID [27]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 03:38:35 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 15

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

\[ y = -\frac {3}{2 x^{3}+1} \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\frac {3}{2 x^3+1} \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = - \frac {3}{2 x^{3} + 1} \]