Question

Question 16:

What is the general solution of the following homogeneous second-order differential equation?

Non-integers are expressed to one decimal place.

d^2y/dx^2 − 11.y = 9

	(a)	y = Ae -3.3.x + Be 3.3.x + 0.82
	(b)	y = Ae -3.3.x + Be 3.3.x - 0.82
	(c)	y = e3.3.x (Ax + B)+0.82
	(d)	y = e3.3.x (Ax + B)- 0.82

Question 17:

What is the general solution of the following homogeneous second order differential equation?

d^2y/dx^2 + 3dy/dx − 4.y = cos(3.x)

	(a)	y = A e1.x + B e4.x - (0.036).sin(3.x) + (-0.052).cos(3.x)
	(b)	y = A e-1.x + B e4.x + (0.036).sin(3.x) - (-0.052).cos(3.x)
	(c)	y = A e1.x + B e-4.x + (0.036).sin(3.x) + (-0.052).cos(3.x)
	(d)	y = A e-1.x + B e-4.x - (0.036).sin(3.x) - (-0.052).cos(3.x)

Question 18:

What is the general solution of the following homogeneous second order differential equation?

d^2y/dx^2 + 13dy/dx + 40.y = sin(2.x)

	(a)	y = A e-5.x + B e-8.x + (0.013).cos(2.x) - (0.018).sin(2.x)
	(b)	y = A e-5.x + B e-8.x - (0.013).cos(2.x) + (0.018).sin(2.x)
	(c)	y = A e-5.x + B e-8.x - (0.013).cos(2.x) - (0.018).sin(2.x)
	(d)	y = A e-5.x + B e-8.x + (0.013).cos(2.x) + (0.018).sin(2.x)

Question 19:

What is the general solution of the following homogeneous second order differential equation?

d^2y/dx^2 + 1dy/dx − 20.y = 1.x − 3

	(a)	y = A e4.x + B e-5.x - 0.050.x - (0.15)
	(b)	y = A e4.x + B e-5.x - 0.050.x + (0.15)
	(c)	y = A e4.x + B e-5.x + 0.050.x - (0.15)
	(d)	y = A e4.x + B e-5.x + 0.050.x + (0.15)

Question 20:

What is the general solution of the following homogeneous second order differential equation?

d^2y/dx^2 − 10dy/dx + 29.y = 1.e(3.x)

	(a)	y = e2.x (A cos(5.x) + B sin (5.x)) + (0.100).e3.x
	(b)	y = A e5.x + B e2.x + (0.015).e3.x
	(c)	y = e-5.x.(A cos(2.x) + B sin (2.x)) - (0.13).e3.x
	(d)	y = e5.x (A cos(2.x ) + B sin (2.x)) + (0.13).e3.x

Answer 1