Internal problem ID [5716]
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]
\[ \boxed {y^{\prime }-\sin \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)=y(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.03 (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*}