Question 3 A lst order ODE has the following form _ 2 3 EGt by The constants a and b are real and positive. What is(are) the dependent variablels) and what is(are) the independent variablels)? Choose the best answer Q) The dependent variables are both y and t, and the independent variables are a and b. O y is the dependent variable, and t is independent variable. 0 t is the dependent variable, and y is independent variable. 0 The dependent variables are a and b, and the independent variables are y and t. Question 4 1 pts A lst order ODE has the following form dy 4 a = 0(y3 b) 6'52 +57% The constants a, b, c, and g are real and positive. Which of the following statements is true? Q The equation can be solved by separation of variables O The equation can be solved with an integrating factor Q The equation cannot be solved by separation of variables. It also cannot be solved with an integrating factor as it nonlinear Q The equation cannot be solved by separation of variables and it cannot be solved with an integrating factor as it nonhomogeneous Question 5 1 A 1st order ODE has the following form 4 = a(y3 - b) - ct2 + gthy The constants a, b, c, and g are real and positive. If y has dimensions of [length] and t has dimensions of [time], what are the dimensions of the constant g? O [length]*[time]^(-1) O [length]*[time] O [length]^(-3)*[time]^(-3) O [time]^(-3)Question 7 1 pts A lst order ODE has the following form d df =a(yb) ct2 +93% The constants a, b , c and g are real and positive. Here, y represents a height and t is time. Using your expressions of P and Q from Question 6, do you get the following form for the general solution? y(t) : (at+gt4/4) (f (ab + ct2)e{atgt4/4) (it) + 08(atlgt4/4) (Note: the integral cannot be analytically integrated in this equation). In this equation, what does C represent? Choose the best answer. Q It is a constant. It can be determined if it at time = O, the value of the height (y) is 10 m. 0 It is a constant. This constant must be given to you in the problem statement. 0 It is a constant. it can be determined if it at time = O, the value of velocity (v) is 10 m/s. 0 It is a constant. it can be determined if it at time = O, the value of velocity (v) is 10 m/s. It can be determined from all the other constants (a,b,c,g) Question 8 As discussed in lecture, the acceleration of a launched roller coaster can be described as d'U Pf Fe a EU = gewmt/To) Is this equation homogeneous? 0 Yes O No, as it has a forcing function O No, as it is nonlinear O No, as it cannot be solved by separation of variables Question 9 1 pts As discussed in lecture, the acceleration of a roller coaster can be described as Can this equation be solved by separation of variables? 0 No, as the equation is not linear. O No, as the equation has a forcing function. 0 No, as there is no way to separate the equation so that all the v variables are on the Ihs and all the tvariables are on the rhs. O No, as the function is not homogenous. 0 Yes, it can be. Question 10 1 pts As discussed in lecture, the acceleration of a roller coaster can be described as (it? Hf _ Fe 5 H\" E Can this equation be solved by separation of variables? (In answering this question, recognize the difference in the forcing function provided in Question 9 vs Question 10.) O No, as the equation is not linear. O No, as the equation has a forcing function. O No, as there is no way to separate the equation so that all the v variables are on the Ihs and all the t variables are on the rhs. O No, as the function is not homogenous. 0 Yes, it can be