6.9.38 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 : Tuesday, September 30, 2025 at 05:19:25 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.326 (sec). Leaf size: 46

ode=D[y[x],x]+y[x]^2+5*y[x]-6==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.236 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + 5*y(x) + Derivative(y(x), x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {6 e^{7 C_{1} - 7 x} + 1}{e^{7 C_{1} - 7 x} - 1} \]