6.9.42 problem 38 part (g)

Internal problem ID [1798]
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 (g)
Date solved : Tuesday, September 30, 2025 at 05:19:28 AM
CAS classification : [_quadrature]

\begin{align*} 36 y^{\prime }+36 y^{2}-12 y+1&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=36*diff(y(x),x)+36*y(x)^2-12*y(x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 +x +6}{6 c_1 +6 x} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 30

ode=36*D[y[x],x]+36*y[x]^2-12*y[x]+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x+6-36 c_1}{6 x-216 c_1}\\ y(x)&\to \frac {1}{6} \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x)**2 - 12*y(x) + 36*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - x - 6}{6 \left (C_{1} - x\right )} \]