The equation - 3y + 10 = -12 cos x + 2 sin x is a second order linear ordinary differential equation. Select one: O True O FalseThe equation - 3ety = -5cos x is a third order nonlinear ordinary differential equation. Select one: True FalseThe direction field of the DE = 4x - 3y will have a line segment with positive slope at the point (2, -1). Select one: O True O FalseThe following graph represents the direction field of the DE y = y. ANAN Select one: True OFalseWhich of the following is a solution to the differential equation? =-7y Select one: O V= -7x O y=7 O y = 7e" O None of theseWhich of the following is a solution to the differential equation? -2y + 16 sin 4x = 0 Select one: O None of these O V= - COS 4x O y= -2 cos 4x O y = 2 cos 2x O y = 2 sin 4xy = 3 is _..... for the autonomous DE: dy dx =9y - y Select one: O semi-stable O None of these O is not a critical point O asymptotically stable O unstableThe critical points of the following autonomous DE are dy = -(y - 4) In(3 - y) dx Select one: O None of these O y = 4, y=3 Oy= 3 O y = 1, y = 4 O y = 2Work Problem. Solve the following questions (write neatly and show step-by step solutions). Question 1 Verify that y = cje + cre-3x is a solution to the DE: 4y - 21y = 0. Question 2 Find a solution to the IVP: V - 4y' - 21y = 0, W0) = -1 and y' (0) = 2 Question 3 Classify each critical point as asymptotically stable, unstable, or semi- stable of the following DE: V - 5y* - 36y