[Second Order Differential Equations] Linear constant-coefficient 2nd order differential are very important in Electrical and Computer Engineering (ECE), yet recitation quiz #5 shows that many of you are still struggling with that concept. Here we start with such a differential equation, first a homogeneous solution and then with a forcing function for which we know the form of the particular solution, but then we move on to a more complicated forcing function and then finally to a problem with time-varying coefficients: Find the entire solution for each of the following: (a) y 00 − 4y 0 + 5y = 0, y(0) = 1, y0 (0) = 0 (b) y 00 − 4y 0 + 5y = 5t 2 , y(0) = 2, y0 (0) = 0 (fractions get a little messy) Find the particular solution to the following using the variation of parameters technique: (a) y 00 − 4y 0 + 5y = e 2t csc t (b) t 2y 00 − 4ty0 + 6y = t −4 .

Accepted Solution

Answer:Please see attachment Step-by-step explanation:Please see attachment