Differential Equations Exam Questions with Correct Answers

Differential Equations Exam Questions with Correct Answers True or False? Every homogeneous linear differential equation always has a solution - Answer-True True or False? In the growth model dP/dt=50e^0.5t, the growth constant is 50 - Answer-False True or False? In the competition model dx/dt = ax-bxy, dy/dt=cy-dxy, where x(t) and y(t) are the popultions of the competing species moose and deer, respectively, the coefficient c represents the moose growth rate - Answer-False True or False? The Wronskian of the function e^x and e^3x is 2e^2x - Answer-False True or False? The differential operator D is a linear operator - Answer-True True or False? A BVP can have exactly two solutions - Answer-False True or False? If a set of two functions is linearly independent, then one function is a constant multiplier of the other - Answer-False True or False? If yp1 and yp2 are solutions of the DE y'' + P(x)y' + Q(x) =0, then y=yp1=yp2 is also a solution to the DE. - Answer-True True or False? If y1,y2,...yn form a FSS of an nth order DE on an interval I, then y1,y2,...yn must be linearly dependent - Answer-False True or False? 3x^4y'' + e^xy' = (tanx)y is a homogeneous differential equation - Answer-True True or False? The differential equation dP/dt=kP is both separable and linear - Answer-True