12.6.30 problem 39

Internal problem ID [1709]
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 : 39
Date solved : Saturday, March 29, 2025 at 11:35:29 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.082 (sec). Leaf size: 30

ode:=diff(y(x),x)-3*y(x)/x = 2*x^4*(4*x^3-3*y(x))/(3*x^5+3*x^3+2*y(x)); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (-3 x^{2}+\sqrt {9 x^{4}+34 x^{2}+21}-3\right ) x^{3}}{2} \]

✓ Mathematica. Time used: 0.749 (sec). Leaf size: 49

ode=D[y[x],x]-3/x*y[x]== (2*x^4*(4*x^3-3*y[x]))/(3*x^5+3*x^3+2*y[x]); 
ic=y[1]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (-3 x^5-3 x^3+\sqrt {\frac {1}{x^7}} \sqrt {x \left (9 x^4+34 x^2+21\right )} x^6\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**4*(4*x**3 - 3*y(x))/(3*x**5 + 3*x**3 + 2*y(x)) + Derivative(y(x), x) - 3*y(x)/x,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out