73.3.9 problem 4.3 (i)

Internal problem ID [15043]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.3 (i)
Date solved : Tuesday, January 28, 2025 at 07:28:23 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 25

dsolve(diff(y(x),x)=sin(x+y(x)),y(x), singsol=all)
 

\[ y = -x -2 \arctan \left (\frac {c_{1} -x -2}{-x +c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 186

DSolve[D[y[x],x]==Sin[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x-\exp \left (\int _1^{K[2]+y(x)}\left (1-\frac {2}{\tan \left (\frac {K[1]}{2}\right )+1}\right )dK[1]\right ) \sin (K[2]+y(x))dK[2]+\int _1^{y(x)}\left (\exp \left (\int _1^{x+K[3]}\left (1-\frac {2}{\tan \left (\frac {K[1]}{2}\right )+1}\right )dK[1]\right )-\int _1^x\left (-\exp \left (\int _1^{K[2]+K[3]}\left (1-\frac {2}{\tan \left (\frac {K[1]}{2}\right )+1}\right )dK[1]\right ) \cos (K[2]+K[3])-\exp \left (\int _1^{K[2]+K[3]}\left (1-\frac {2}{\tan \left (\frac {K[1]}{2}\right )+1}\right )dK[1]\right ) \sin (K[2]+K[3]) \left (1-\frac {2}{\tan \left (\frac {1}{2} (K[2]+K[3])\right )+1}\right )\right )dK[2]\right )dK[3]=c_1,y(x)\right ] \]