The following require little or no computation or are TRUEFA

The following require little or no computation or are TRUE/FALSE questions. justify your answers Every separable differential equation is linear (T/F). Give an example of a first-order differential equation that has the function y(t) = 3t + 2 as a solution. Convert the second-order equationd^2y/dt^2 = -1 to a first-order system. Sketch the solution curve for the initial value problem dx/dt = -x, dy/dt = -y, and (x(0),y(0)) = (-1,-1). The origin is the only equilibrium point for any linear system (T/F). Classify the equilibrium point (e.g. sink, source, center, etc.) of the linear system d8/dt = [-1 2 -2 0]8. For which values of omega is the forced harmonic oscillator d^2y/dt^2 + 9y = cos(omega t) in resonance Suppose a friend solves the initial-value problem d^2y/dt^2 + 7dy/dt + 6y = sin(3t) - 2 cos(3t), y(0) = 1, y\'(0) = 1 and the solution has large amplitude oscillations when t is large. How do you immediately know your friend has made a mistake

Solution

a) Every separable differential is not linear.. So answer is false

b) Example to get the solution y(t) = 3t+2

If equation is 3/2(t^2)+2t+6 solution will be as required