7.3.26 problem 26

Internal problem ID [66]
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 1.4 (separable equations). Problems at page 43
Problem number : 26
Date solved : Tuesday, March 04, 2025 at 10:41:26 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: 0.023 (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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.136 (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]
 

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

✓ Sympy. Time used: 0.180 (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)
 

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