Internal problem ID [13148]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\tan \left (6 x +3 y+1\right )=-2} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 185
dsolve(diff(y(x),x)=tan(6*x+3*y(x)+1)-2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\arctan \left (c_{1} {\mathrm e}^{3 x}, {\mathrm e}^{6 x} c_{1}^{2} \sqrt {\frac {{\mathrm e}^{-6 x} \left (\frac {{\mathrm e}^{-6 x}}{c_{1}^{2}}-1\right )}{c_{1}^{2}}}\right )}{3}-2 x -\frac {1}{3} y \left (x \right ) = \frac {\arctan \left (c_{1} {\mathrm e}^{3 x}, -{\mathrm e}^{6 x} c_{1}^{2} \sqrt {\frac {{\mathrm e}^{-6 x} \left (\frac {{\mathrm e}^{-6 x}}{c_{1}^{2}}-1\right )}{c_{1}^{2}}}\right )}{3}-2 x -\frac {1}{3} y \left (x \right ) = \frac {\arctan \left (-c_{1} {\mathrm e}^{3 x}, {\mathrm e}^{6 x} c_{1}^{2} \sqrt {\frac {{\mathrm e}^{-6 x} \left (\frac {{\mathrm e}^{-6 x}}{c_{1}^{2}}-1\right )}{c_{1}^{2}}}\right )}{3}-2 x -\frac {1}{3} y \left (x \right ) = \frac {\arctan \left (-c_{1} {\mathrm e}^{3 x}, -{\mathrm e}^{6 x} c_{1}^{2} \sqrt {\frac {{\mathrm e}^{-6 x} \left (\frac {{\mathrm e}^{-6 x}}{c_{1}^{2}}-1\right )}{c_{1}^{2}}}\right )}{3}-2 x -\frac {1}{3} \end{align*}
✓ Solution by Mathematica
Time used: 60.483 (sec). Leaf size: 25
DSolve[y'[x]==Tan[6*x+3*y[x]+1]-2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (\arcsin \left (e^{3 x-3 c_1}\right )-6 x-1\right ) \]