Question 13 (12 marks) Consider the following separable differential equation. dy -cos (y)e-z (a) Find the...

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Question 13 (12 marks) Consider the following separable differential equation. dy -cos² (y)e-z (a) Find the constant (or equilibrium) solutions of this differential equation. There are infinitely many of them! (b) Use your answer to (a) to write down the solution with initial value y = when x = 0. (c) What does the answer to (a) tell us about the range of solution with initial value y = 0 when x=0? dr (d) Use the method for solving separable differential equations to solve this equation in the case where - < y<. [Hint: Recall from lectures that tan'(x) = sec²(x).] (e) Use your answer to (d) to find the solutions with the following initial values: (i) y = 0 when x = 0. (ii) y = when x = 0. (f) What is the solution for the initial value y = when z = 0? Explain why this is not one of the solutions you found in part (d). Question 13 (12 marks) Consider the following separable differential equation. dy -cos² (y)e-z (a) Find the constant (or equilibrium) solutions of this differential equation. There are infinitely many of them! (b) Use your answer to (a) to write down the solution with initial value y = when x = 0. (c) What does the answer to (a) tell us about the range of solution with initial value y = 0 when x=0? dr (d) Use the method for solving separable differential equations to solve this equation in the case where - <y<. [Hint: Recall from lectures that tan'(x)= sec² (r).] (e) Use your answer to (d) to find the solutions with the following initial values: (i) y 0 when x = 0. = (ii) y = when x = 0. (f) What is the solution for the initial value y = when z = 0? Explain why this is not one of the solutions you found in part (d). Question 13 (12 marks) Consider the following separable differential equation. dy -cos² (y)e-z (a) Find the constant (or equilibrium) solutions of this differential equation. There are infinitely many of them! (b) Use your answer to (a) to write down the solution with initial value y = when x = 0. (c) What does the answer to (a) tell us about the range of solution with initial value y = 0 when x=0? dr (d) Use the method for solving separable differential equations to solve this equation in the case where - < y<. [Hint: Recall from lectures that tan'(x) = sec²(x).] (e) Use your answer to (d) to find the solutions with the following initial values: (i) y = 0 when x = 0. (ii) y = when x = 0. (f) What is the solution for the initial value y = when z = 0? Explain why this is not one of the solutions you found in part (d). Question 13 (12 marks) Consider the following separable differential equation. dy -cos² (y)e-z (a) Find the constant (or equilibrium) solutions of this differential equation. There are infinitely many of them! (b) Use your answer to (a) to write down the solution with initial value y = when x = 0. (c) What does the answer to (a) tell us about the range of solution with initial value y = 0 when x=0? dr (d) Use the method for solving separable differential equations to solve this equation in the case where - <y<. [Hint: Recall from lectures that tan'(x)= sec² (r).] (e) Use your answer to (d) to find the solutions with the following initial values: (i) y 0 when x = 0. = (ii) y = when x = 0. (f) What is the solution for the initial value y = when z = 0? Explain why this is not one of the solutions you found in part (d).

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a To find the constant solutions we set the derivative equal to zero dydx cos2yex 0 This equation is ... View the full answer