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Choose the correct answers If y1 and y2 are two solutions of a nonhomogeneous equation ayjj+...

Choose the correct answers

  1. If y1 and y2 are two solutions of a nonhomogeneous equation ayjj+ byj+ cy =f (x), then their difference is a solution of the equation ayjj+ byj+ cy = 0.
  2. If f (x) is continuous everywhere, then there exists a unique solution to the following initial value problem.

                                  f (x)yj= y,   y(0) = 0

  1. The differential equation yjj + t2yj − y = 3 is linear.
  2. There is a solution to the ODE yjj+3yj+y = cos 6t of the form yp(t) = A cos 6t.
  3. Critical points or equilibrium points for a first order ordinary differential equation yj(t) = f (t, y) are those points where the solution is zero or where the slope of the solution is a constant everywhere.
  4. The ODE dy /dt − ty + t = (y − 1)(y − t) is autonomous.
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