a) Solve the following differential equation.b) find the offset that maximizes the stroke if the offset must not exceed the radius of the circle.

(a) Solve the following differential equation: dy + 2y = e -*sinc (b) Slider-cranks, such as that shown below, transform rotary motion to back-and- forthmotion along a straight line, and vice versa, Rod AB, of length r, is pinned at A, and rod BC, of length L, is pinned to rod AB at B, As AB rotates around A, C is confined to move along a horizontal line segment between points D and E, called the stroke of the mechanism. Rotary motion of B is transformed to straight-line motion of C along DE. This crank is said to be offset because the extension of line segment DE does not pass through the centre of the circle A; it is offset by an amount e. Find the offset that maximizes the stroke if the offset must not exceed the radius of the circle. (10 marks) -. B L E D Page 3 of 3