73.5.16 problem 6.7 (d)

Internal problem ID [15048]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (d)
Date solved : Thursday, March 13, 2025 at 05:31:59 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 19

ode:=diff(y(x),x) = 4+1/sin(4*x-y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 4 x -\frac {\pi }{2}-\arcsin \left (-x +c_{1} \right ) \]

✓ Mathematica. Time used: 0.315 (sec). Leaf size: 101

ode=D[y[x],x]==4+1/Sin[4*x-y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x(\csc (4 K[1]-y(x))+4) \sin (4 K[1]-y(x))dK[1]+\int _1^{y(x)}\left (-\sin (4 x-K[2])-\int _1^x(\cot (4 K[1]-K[2])-\cos (4 K[1]-K[2]) (\csc (4 K[1]-K[2])+4))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 3.243 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 4 - 1/sin(4*x - y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 4 x + \operatorname {acos}{\left (C_{1} + x \right )}, \ y{\left (x \right )} = 4 x - \operatorname {acos}{\left (C_{1} + x \right )} + 2 \pi \right ] \]