12.5.53 problem 52

Internal problem ID [1677]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 52
Date solved : Saturday, March 29, 2025 at 11:26:43 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 x^{2} y^{2}+6 x y+2}{x^{2} \left (2 x y+3\right )} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.077 (sec). Leaf size: 18

ode:=diff(y(x),x)+2*y(x)/x = (3*x^2*y(x)^2+6*x*y(x)+2)/x^2/(2*x*y(x)+3); 
ic:=y(2) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {-3+\sqrt {1+60 x}}{2 x} \]

✓ Mathematica. Time used: 0.736 (sec). Leaf size: 35

ode=D[y[x],x]+2/x*y[x]==(3*x^2*y[x]^2+6*x*y[x]+2)/(x^2*(2*x*y[x]+3)); 
ic=y[2]==2; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sqrt {\frac {1}{x^2}} \sqrt {x^2 (60 x+1)}-3}{2 x} \]

✓ Sympy. Time used: 0.950 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 2*y(x)/x - (3*x**2*y(x)**2 + 6*x*y(x) + 2)/(x**2*(2*x*y(x) + 3)),0) 
ics = {y(2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {60 x + 1} - 3}{2 x} \]