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 : Tuesday, March 04, 2025 at 01:42:23 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.55 (sec). Leaf size: 47

ode=D[y[x],x]+y[x]^2+8*y[x]+7==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.381 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + 8*y(x) + Derivative(y(x), x) + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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