10.5.4 problem 4

Internal problem ID [1196]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 4
Date solved : Saturday, March 29, 2025 at 10:45:42 PM
CAS classification : [_separable]

\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=2*y(x)+2*x*y(x)^2+(2*x+2*x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{x} \\ y &= \frac {-1-c_1}{x} \\ y &= \frac {-1+c_1}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 29

ode=2*y[x]+2*x*y[x]^2+(2*x+2*x^2*y[x])*D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = \frac {C_{1}}{x} \]