73.3.15 problem 4.4 (e)

Internal problem ID [15049]
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 : 4.4 (e)
Date solved : Tuesday, January 28, 2025 at 07:28:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

dsolve(cos(y(x))*diff(y(x),x)=sin(x),y(x), singsol=all)
 

\[ y = \arcsin \left (-\cos \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 31

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

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\int _1^x\sin (K[2])dK[2]+c_1\right ] \]