Assignment_1

Assignment_1 - Question 3. Solve the following Cauchy-Euler...

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ME 303 ADVANCED ENGINEERING MATHEMATICS Assignment 1 Question 1. Solve the following first-order, initial value problem for 0 : ) ( = + y dt dy t y β with 3 ) 0 ( = y for three cases: (a) the parameter 0 = (b) the parameter is positive, say 4 = (c) the parameter is negative, say 4 = Sketch the solutions obtained in (a)-(c) on one graph. Question 2. Consider the following second-order ODE 0 2 2 = + y dt y d . (a) Find ) ( t y if 0 = and ICs are 5 ) 0 ( = y , 1 ) 0 ( = dt dy (b) Find ) ( t y if 4 = and ICs are 4 ) 0 ( = y , 2 ) 0 ( = dt dy . Express the solution in two forms, the complex exponential form and the sine/cosine form. (c) Find ) ( t y if 4 = and ICs are 3 ) 0 ( = y , 0 ) 0 ( = dt dy . Express the solution in two forms, the complex exponential form and the sinh/cosh form.
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Unformatted text preview: Question 3. Solve the following Cauchy-Euler ODE : A y xy y x = + 2 ' 2 " 2 , with ICs given by 1 ) ( ' = y and 1 ) ( " = y , for the following two cases (a) = A (b) 2 = A Question 4. Consider the following ODE: ' " = + + xy y xy . By simply recognizing the form of the ODE, write down the general solution (do NOT do the detailed algebra associated with the Frobenius method). For the following ICs: 1 ) ( = y , ) ( ' = y , find the solution ) ( x y and sketch it (see ME 203 text pp 487-489 and handout)....
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