9.38 problem 38 part (c)

Internal problem ID [1144]

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 (c).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }+y^{2}+5 y-6=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve(diff(y(x),x)+y(x)^2+5*y(x)-6=0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {6+{\mathrm e}^{7 x} c_{1}}{{\mathrm e}^{7 x} c_{1}-1} \]

Solution by Mathematica

Time used: 0.677 (sec). Leaf size: 34

DSolve[y'[x]+y[x]^2+5*y[x]-6==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-5+7 \coth \left (\frac {7 (x-c_1)}{2}\right )\right ) \\ y(x)\to -6 \\ y(x)\to 1 \\ \end{align*}