Consider the system of differential equations with initial values: 2 y = y + sint; = x + 2 cost; (0) = 0 y(0) = 0 solve this system with the following indicating methods: a: by the method of laplace transforms. b: simplify it by differentiating one of the equation and then substitute to the other equation to form a 2nd order linear differential equation with constant coefficients. find this 2nd order ode with the corresponding initial values. (make sure you write down two initial conditions.) c: solve the 2nd order ode in part b with method of undetermined coefficients. (for the purpose of reviewing for the final exam)