9.42 problem 38 part (g)

Internal problem ID [1148]

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).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {36 y^{\prime }+36 y^{2}-12 y+1=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

\[ y \relax (x ) = \frac {c_{1}+x +6}{6 c_{1}+6 x} \]

Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 24

DSolve[36*y'[x]+36*y[x]^2-12*y[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

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