12.9.39 problem 38 part (d)

Internal problem ID [1795]
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)
Date solved : Monday, January 27, 2025 at 05:35:00 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}+8 y+7&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve(diff(y(x),x)+y(x)^2+8*y(x)+7=0,y(x), singsol=all)
 

\[ y = \frac {7-c_1 \,{\mathrm e}^{6 x}}{c_1 \,{\mathrm e}^{6 x}-1} \]

✓ Solution by Mathematica

Time used: 0.550 (sec). Leaf size: 47

DSolve[D[y[x],x]+y[x]^2+8*y[x]+7==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^{6 x}-7 e^{6 c_1}}{e^{6 x}-e^{6 c_1}} \\ y(x)\to -7 \\ y(x)\to -1 \\ \end{align*}