Internal problem ID [1147]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {6 y^{\prime }+6 y^{2}-y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve(6*diff(y(x),x)+6*y(x)^2-y(x)-1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1+{\mathrm e}^{\frac {5 x}{6}} c_{1}}{2 \,{\mathrm e}^{\frac {5 x}{6}} c_{1}-3} \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 45
DSolve[6*y'[x]+6*y[x]^2-y[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3}+\frac {1}{\frac {6}{5}+\frac {9}{5} e^{-\frac {5 x}{6}+5 c_1}} \\ y(x)\to -\frac {1}{3} \\ y(x)\to \frac {1}{2} \\ \end{align*}