64.3.5 problem 5

Internal problem ID [13205]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:37:29 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 69

ode:=6*x*y(x)+2*y(x)^2-5+(3*x^2+4*x*y(x)-6)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-3 x^{2}+6+\sqrt {9 x^{4}-8 c_1 x +4 x^{2}+36}}{4 x} \\ y &= \frac {-3 x^{2}+6-\sqrt {9 x^{4}-8 c_1 x +4 x^{2}+36}}{4 x} \\ \end{align*}

✓ Mathematica. Time used: 0.608 (sec). Leaf size: 79

ode=(6*x*y[x]+2*y[x]^2-5)+(3*x^2+4*x*y[x]-6)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}-6}{4 x} \\ y(x)\to \frac {-3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}+6}{4 x} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x*y(x) + (3*x**2 + 4*x*y(x) - 6)*Derivative(y(x), x) + 2*y(x)**2 - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out