Internal problem ID [13034]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page
103
Problem number: 5.1 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\sin \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)=y(x)*sin(x),y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 19
DSolve[y'[x]==y[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\cos (x)} y(x)\to 0 \end{align*}