Question

Choose the correct answers

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

                                  f (x)y^j= y,   y(0) = 0

3. The differential equation y^jj + t²y^j − y = 3 is linear.
4. There is a solution to the ODE y^jj+3y^j+y = cos 6t of the form y_p(t) = A cos 6t.
5. Critical points or equilibrium points for a first order ordinary differential equation y^j(t) = f (t, y) are those points where the solution is zero or where the slope of the solution is a constant everywhere.
6. The ODE dy /dt − ty + t = (y − 1)(y − t) is autonomous.

Answer 1