Internal problem ID [13402]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\sin \left (y\right )={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(cos(y(x))*diff(y(x),x)=exp(-x)-sin(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (\left (c_{1} -x \right ) {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 11.73 (sec). Leaf size: 16
DSolve[Cos[y[x]]*y'[x]==Exp[-x]-Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (e^{-x} (x+c_1)\right ) \]