Question

Verify that the trajectory family x(t, Ω) satisfies the boundary conditions by direct substitution?

Answer 1

To verify the trajectory family x(t, Ω) satisfies the boundary conditions, substitute the values of t and Ω into the equation and check if it satisfies the condition.

Step-by-step explanation:

To verify that the trajectory family x(t, Ω) satisfies the boundary conditions by direct substitution, we substitute the given values of t and Ω into the equation for x(t, Ω). We then check if the resulting expression satisfies the boundary conditions.

For example, if the boundary condition is x(0) = 0, we substitute t = 0 into the equation x(t, Ω) and check if the resulting expression equals 0.

If the expression satisfies the boundary conditions for all values of t and Ω, we can conclude that the trajectory family x(t, Ω) satisfies the boundary conditions.