2.3.25 problem 26

Internal problem ID [701]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 04:06:30 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 16

ode:=diff(y(x),x) = 2*x*y(x)^2+3*x^2*y(x)^2; 
ic:=[y(1) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 17

ode=D[y[x],x] == 2*x*y[x]^2+3*x^2*y[x]^2; 
ic=y[1]==-1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2*y(x)**2 - 2*x*y(x)**2 + Derivative(y(x), x),0) 
ics = {y(1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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