2.2.9 problem 11

Internal problem ID [669]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:05:15 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: 0.066 (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: 0.091 (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)
 

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