Final answer:
The differential equation y′=2y+sinx is of the linear type, as it fits the definition of a linear differential equation.
Step-by-step explanation:
The differential equation y′=2y+sinx is a linear differential equation. Linear equations can be identified by their standard form, y = mx + b, where m is the slope and b is the y-intercept, and they describe a straight line on a graph. In the context of differential equations, a linear equation is an equation that involves the first derivative of the function and the function itself, both multiplied by functions of the independent variable (in this case, x) or constants, but not multiplied together or involving higher derivatives. The given equation is linear because it can be rewritten in the form y′ − 2y = sin(x), showing that the terms involving y are not multiplied by one another and only the first derivative of y is present.