76.1.19 problem 19

Internal problem ID [17247]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 19
Date solved : Monday, March 31, 2025 at 03:46:12 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 20

ode:=diff(y(x),x) = 2*x*y(x)^2+4*x^3*y(x)^2; 
ic:=y(1) = -2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {2}{2 x^{4}+2 x^{2}-3} \]

✓ Mathematica. Time used: 0.165 (sec). Leaf size: 21

ode=D[y[x],x]==2*x*y[x]^2+4*x^3*y[x]^2; 
ic={y[1]==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {2}{2 x^4+2 x^2-3} \]

✓ Sympy. Time used: 0.190 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3*y(x)**2 - 2*x*y(x)**2 + Derivative(y(x), x),0) 
ics = {y(1): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {1}{x^{4} + x^{2} - \frac {3}{2}} \]