12.9.38 problem 38 part (c)

Internal problem ID [1794]
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)
Date solved : Monday, January 27, 2025 at 05:34:58 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}+5 y-6&=0 \end{align*}

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.560 (sec). Leaf size: 46

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

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