Internal problem ID [13058]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _dAlembert]
\[ \boxed {\cos \left (-4 y+8 x -3\right ) y^{\prime }-2 \cos \left (-4 y+8 x -3\right )=2} \]
✓ Solution by Maple
Time used: 0.016 (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: 64.647 (sec). Leaf size: 1165
DSolve[Cos[4*y[x]-8*x+3]*y'[x]==2+2*Cos[4*y[x]-8*x+3],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {1}{2} \sqrt {2-\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to \arccos \left (-\frac {1}{2} \sqrt {2-\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to -\arccos \left (\frac {1}{2} \sqrt {2-\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to \arccos \left (\frac {1}{2} \sqrt {2-\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to -\arccos \left (-\frac {1}{2} \sqrt {2+\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to \arccos \left (-\frac {1}{2} \sqrt {2+\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to -\arccos \left (\frac {1}{2} \sqrt {2+\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to \arccos \left (\frac {1}{2} \sqrt {2+\sqrt {-2 \sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+8 (2 x+c_1) \sin (3-8 x)+2}}\right ) y(x)\to -\arccos \left (-\frac {1}{2} \sqrt {2-\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to \arccos \left (-\frac {1}{2} \sqrt {2-\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to -\arccos \left (\frac {1}{2} \sqrt {2-\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to \arccos \left (\frac {1}{2} \sqrt {2-\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to -\arccos \left (-\frac {1}{2} \sqrt {2+\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to \arccos \left (-\frac {1}{2} \sqrt {2+\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to -\arccos \left (\frac {1}{2} \sqrt {2+\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) y(x)\to \arccos \left (\frac {1}{2} \sqrt {2+\sqrt {2} \sqrt {\sqrt {-\left (\left (64 x^2+64 c_1 x-1+16 c_1{}^2\right ) \cos ^2(3-8 x)\right )}+4 (2 x+c_1) \sin (3-8 x)+1}}\right ) \end{align*}