73.5.3 problem 6.1 (c)

Internal problem ID [15114]
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 : Tuesday, January 28, 2025 at 07:31:29 AM
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*}

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 19

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

\[ y = 2 x -\frac {3}{4}-\frac {\arcsin \left (-8 x +8 c_{1} \right )}{4} \]

✓ Solution by Mathematica

Time used: 2.092 (sec). Leaf size: 23

DSolve[Cos[4*y[x]-8*x+3]*D[y[x],x]==2+2*Cos[4*y[x]-8*x+3],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} (\arcsin (4 (2 x+c_1))+8 x-3) \]