73.7.46 problem 46

Internal problem ID [15133]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 46
Date solved : Monday, March 31, 2025 at 01:26:42 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 35

ode:=diff(y(x),x) = tan(6*x+3*y(x)+1)-2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2 x -\frac {1}{3}-\frac {\operatorname {arccsc}\left ({\mathrm e}^{-3 x} c_1 \right )}{3} \\ y &= -2 x -\frac {1}{3}+\frac {\operatorname {arccsc}\left ({\mathrm e}^{-3 x} c_1 \right )}{3} \\ \end{align*}

✓ Mathematica. Time used: 60.444 (sec). Leaf size: 25

ode=D[y[x],x]==Tan[6*x+3*y[x]+1]-2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} \left (\arcsin \left (e^{3 x-3 c_1}\right )-6 x-1\right ) \]

✓ Sympy. Time used: 9.417 (sec). Leaf size: 73

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(6*x + 3*y(x) + 1) + Derivative(y(x), x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 2 x - \frac {\operatorname {atan}{\left (\sqrt {- \frac {e^{6 C_{1} + 6 x}}{e^{6 C_{1} + 6 x} - 1}} \right )}}{3} - \frac {1}{3}, \ y{\left (x \right )} = - 2 x + \frac {\operatorname {atan}{\left (\sqrt {- \frac {e^{6 C_{1} + 6 x}}{e^{6 C_{1} + 6 x} - 1}} \right )}}{3} - \frac {1}{3}\right ] \]