12.6.29 problem 38

Internal problem ID [1708]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 38
Date solved : Saturday, March 29, 2025 at 11:35:24 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=-\frac {2 x y}{x^{2}+2 x^{2} y+1} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.702 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{2} \left (-\frac {1}{x^2}-\frac {\sqrt {x^3 \left (x^2+1\right )^2}}{x^{7/2}}-1\right ) \]

✗ Sympy

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

Timed Out