Internal problem ID [4963]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\sin \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve(diff(y(x),x)=y(x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\cos \relax (x )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.05 (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*}