Internal problem ID [1145]
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 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}+8 y+7=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x)+y(x)^2+8*y(x)+7=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-7+{\mathrm e}^{6 x} c_{1}}{{\mathrm e}^{6 x} c_{1}-1} \]
✓ Solution by Mathematica
Time used: 0.688 (sec). Leaf size: 28
DSolve[y'[x]+y[x]^2+8*y[x]+7==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4+3 \coth (3 (x-c_1)) \\ y(x)\to -7 \\ y(x)\to -1 \\ \end{align*}