Which of the following methods that have been covered in the

Which of the following methods that have been covered in the class can be used to solve the initial value problem, y\" + 3y\' + 2y = e^-3t, y\' (0) = 1, y (0) = 0 method of undetermined coefficients method of variation of parameters method of order reduction A and B A and C B and C A, B and C only one of the three

Solution

A. ie method of undetermined coefficients can be used because we have we have an associated homogneous ode which can be solved and using the inhomogenous part is exp^{-3x} we can guess particular soluton as: Cexp(-3x) . C can be solved for by substituting in ode.

B. Again we can solve the associated homogeneous ode and using that we can guess the particular soluton eg. Let, c1y1+c2y2 be general soluton to homogneous ode

then guess for particular solution is

P(x)y1+Q(x)y2

C cannot be used as in this method we must have a solution to start with. But we are not given a soluton in the problem so we cannot use this method.

So,

a) A and B