Hello, Could you please solve all these practice questions for my real analysis math class?

Math 3410 Exam 2 Review Sheet Conley, Spring 2022 The exam will have about 7 problems and one extra-credit problem. You will need to simplify all answers as much as possible. You will be given the following formulas: [ ( f ) ( s ) = So e-st f ( t ) dt , [ (ebt f ) = [(f) (s- b), [ (tf ) = - if(f ). L luc ( t ) f ( t - c ) ) ( s ) = e- scf ( f ) ( s ) , [ (y " + ay' + by ) = (82 + as + b ) Y - (s + a)y(0) - y'(0). 1. Consider y" + 3y' - 10y = g(t) with ICs y(0) = 1, y'(0) = 2. (a) Let g = 84e-t. Find Y(s), apply partial fractions, and then find y(t). (b) Let g = 49e2t. Find Y(s), apply partial fractions, and then find y(t). 2. (a) Find L(est ( sin 2t + cos 2t) ). (b) Find L(the -2t). (c) Find [(h), where h(t) = 1 for 1