Boundary Value Problems and Differential Equations

What is the initial condition given for X at zero?

• X of zero equals one

• X of zero equals zero

• X prime of zero equals one

• X prime of zero equals zero

What type of differential equation is being solved in this problem?

• Second order nonlinear

• First order nonlinear

• Second order linear

• First order linear

What is the characteristic equation derived from the given differential equation?

• r squared minus one equals zero

• r squared plus one equals zero

• r squared plus two equals zero

• r squared minus two equals zero

What are the roots of the characteristic equation?

• Plus or minus one

• Plus or minus two

• Plus or minus i

• Plus or minus zero

What form does the general solution take given the roots of the characteristic equation?

• X of T equals a e to the t plus b e to the minus t

• X of T equals a t plus b

• X of T equals a cosine t plus b sine t

• X of T equals a sine t plus b cosine t

What does the first boundary condition X of zero equals zero imply about the constant 'a'?

• a equals zero

• a equals two

• a equals one

• a equals negative one

What is the derivative of the general solution X of T equals B sine t?

• Negative B sine t

• B cosine t

• Negative B cosine t

• B sine t

What does the second boundary condition X prime of pi equals one imply about the constant 'b'?

• b equals two

• b equals negative one

• b equals zero

• b equals one

What is the final solution to the boundary value problem?

• X of T equals negative sine t

• X of T equals cosine t

• X of T equals negative cosine t

• X of T equals sine t

What is the value of cosine pi used in the second boundary condition?

• Two

• Negative one

• One

• Zero