73.7.46 problem 46

Internal problem ID [15204]
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
Date solved : Tuesday, January 28, 2025 at 07:42:04 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \end{align*}

✓ Solution by Maple

Time used: 0.230 (sec). Leaf size: 35

dsolve(diff(y(x),x)=tan(6*x+3*y(x)+1)-2,y(x), singsol=all)
 

\begin{align*} y &= -2 x -\frac {1}{3}-\frac {\operatorname {arccsc}\left (c_{1} {\mathrm e}^{-3 x}\right )}{3} \\ y &= -2 x -\frac {1}{3}+\frac {\operatorname {arccsc}\left (c_{1} {\mathrm e}^{-3 x}\right )}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.444 (sec). Leaf size: 25

DSolve[D[y[x],x]==Tan[6*x+3*y[x]+1]-2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (\arcsin \left (e^{3 x-3 c_1}\right )-6 x-1\right ) \]