6.9.40 problem 38 part (e)

Internal problem ID [1796]
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 (e)
Date solved : Tuesday, September 30, 2025 at 05:19:26 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}+14 y+50&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=diff(y(x),x)+y(x)^2+14*y(x)+50 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -7-\tan \left (x +c_1 \right ) \]

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 30

ode=D[y[x],x]+y[x]^2+14*y[x]+50==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -7-\tan (x-c_1)\\ y(x)&\to -7-i\\ y(x)&\to -7+i \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + 14*y(x) + Derivative(y(x), x) + 50,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \tan {\left (C_{1} - x \right )} - 7 \]