67.5.3 problem 6.1 (c)

Internal problem ID [16401]
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 : 6.1 (c)
Date solved : Thursday, October 02, 2025 at 01:27:54 PM
CAS classification : [[_homogeneous, `class C`], _exact, _dAlembert]

\begin{align*} \cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 19

ode:=cos(-4*y(x)+8*x-3)*diff(y(x),x) = 2+2*cos(-4*y(x)+8*x-3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 x -\frac {3}{4}-\frac {\arcsin \left (-8 x +8 c_1 \right )}{4} \]

✓ Mathematica. Time used: 1.51 (sec). Leaf size: 23

ode=Cos[4*y[x]-8*x+3]*D[y[x],x]==2+2*Cos[4*y[x]-8*x+3]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} (\arcsin (4 (2 x+c_1))+8 x-3) \end{align*}

✓ Sympy. Time used: 13.174 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(cos(-8*x + 4*y(x) + 3)*Derivative(y(x), x) - 2*cos(-8*x + 4*y(x) + 3) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 2 x + \frac {\operatorname {asin}{\left (C_{1} + 8 x \right )}}{4} - \frac {3}{4}, \ y{\left (x \right )} = 2 x - \frac {\operatorname {asin}{\left (C_{1} + 8 x \right )}}{4} - \frac {3}{4} + \frac {\pi }{4}\right ] \]