73.5.27 problem 6.7 (o)

Internal problem ID [15138]
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 : 6.7 (o)
Date solved : Tuesday, January 28, 2025 at 07:36:28 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 11.765 (sec). Leaf size: 16

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

\[ y(x)\to \arcsin \left (e^{-x} (x+c_1)\right ) \]