Internal problem ID [13391]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {1}{\sin \left (4 x -y\right )}=4} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 19
dsolve(diff(y(x),x)=4+1/sin(4*x-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = 4 x -\frac {\pi }{2}-\arcsin \left (c_{1} -x \right ) \]
✓ Solution by Mathematica
Time used: 0.624 (sec). Leaf size: 33
DSolve[y'[x]==4+1/Sin[4*x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 4 x-\arccos (x-c_1) \\ y(x)\to 4 x+\arccos (x-c_1) \\ \end{align*}