12.6.18 problem 18

Internal problem ID [1697]
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 : 18
Date solved : Saturday, March 29, 2025 at 11:34:37 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 22

ode:=4*x^3*y(x)^2-6*x^2*y(x)-2*x-3+(2*x^4*y(x)-2*x^3)*diff(y(x),x) = 0; 
ic:=y(1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.785 (sec). Leaf size: 31

ode=(4*x^3*y[x]^2-6*x^2*y[x]-2*x-3)+(2*x^4*y[x]-2*x^3)*D[y[x],x]==0; 
ic=y[1]==3; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*y(x)**2 - 6*x**2*y(x) - 2*x + (2*x**4*y(x) - 2*x**3)*Derivative(y(x), x) - 3,0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out