[b]A differential Equation represents a family of curves (solutions)[br][/b][b][br][math]\frac{dy}{dx}=sinx[/math][br][br][math]y=-cosx+c[/math][br][br]where [/b][math]c[/math][b] is the arbitrary constant[br][br]For each [/b][math]c\in R[/math][b] , we have a solution to the given differential equations[/b]

[size=150][math]y=ke^{-cosx}[/math] satisfies y'=y sinx[/size]