12.9.41 problem 38 part (f)

Internal problem ID [1797]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 38 part (f)
Date solved : Tuesday, March 04, 2025 at 01:42:28 PM
CAS classification : [_quadrature]

\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 24

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

\[ y = \frac {1+{\mathrm e}^{\frac {5 x}{6}} c_1}{2 \,{\mathrm e}^{\frac {5 x}{6}} c_1 -3} \]

✓ Mathematica. Time used: 0.216 (sec). Leaf size: 56

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

\begin{align*} y(x)\to \frac {e^{5 x/6}-e^{5 c_1}}{2 e^{5 x/6}+3 e^{5 c_1}} \\ y(x)\to -\frac {1}{3} \\ y(x)\to \frac {1}{2} \\ \end{align*}

✓ Sympy. Time used: 0.332 (sec). Leaf size: 26

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

\[ x + \frac {6 \log {\left (y{\left (x \right )} - \frac {1}{2} \right )}}{5} - \frac {6 \log {\left (y{\left (x \right )} + \frac {1}{3} \right )}}{5} = C_{1} \]