Assignment 1: SEP291 Engineering Modelling (Submission due: 18 December 2017) (Form of submission: online submission in PDF format via the unit site) 1. Identify Ordinary Differential Equations (ODEs) and write the ODEs in the form of either or a. b. c. d. e. f. 2. Give a summary of the main steps of doing mathematical modelling for one engineering system that you know. 3. Classify the following DEs as linear homogeneous, linear nonhomogeneous or nonlinear differential equations. Also state their order and name the dependent and independent variables. a. b. c. d. 4. Verify that , where c is an arbitrary constant, is a solution of the following ODE, 5. Verify that the following first-order ODE is of separable form. Then solve it to have a general solution. 6. Verify that the following first-order ODE belongs to the form of dx/dt=f(x/t). If so, solve it together with the given initial condition (initial-value problem). 7. Test that the following first-order ODE is of exact form (this test is also called the exactness test). If so, find the general solution. 8. Verify that the following first-order ODE is a linear differential equation. If so, solve for its initial-value problem. 9. Using the Euler’s method with a step size of h=0.1, find the value of X(0.3) for the initialvalue problem 10. Find the general solution of the following differential equation: 11. Find the general solution of the following differential equation:
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