Question 11:
What is the general solution of the following homogeneous second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a) |
y = e 12.5.x (Ax + B) |
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(b) |
y = e -5.x (Ax + B) |
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(c) |
y = e -10.x (Ax + B) |
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(d) |
y = e +5.x (Ax + B) |
Question 12:
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 − 38.y =0
(a) |
y = e -6.2.x (Ax + B) |
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(b) |
y = e -6.2.x(A.sin(6.2.x)+ B.cos(6.2.x)) |
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(c) |
y = e 6.2.x (Ax + B) |
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(d) |
y = Ae -6.2.x + Be 6.2.x |
Question 13:
What is the general solution of the following homogeneous second order differential equation?
d2^y/dx^2 − 4dy/dx + 13.y = 0
(a) |
y = A e2.x + B e3.x |
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(b) |
y = e2.x (A cos(3.x ) + B sin (3.x)) |
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(c) |
y = e-2.x.(A cos(3.x) + B sin (3.x)) |
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(d) |
y = e3.x (A cos(2.x) + B sin (2.x)) |
Question 14:
What is the general solution of the following homogeneous second order differential equation?
d^2y/dx^2 + 9 dy/dx + 20.y = 0
(a) |
y = A e4.x + B e-5.x |
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(b) |
y = A e4.x + B e5.x |
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(c) |
y = A e-4.x + B e-5.x |
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(d) |
y = A e-4.x + B e5.x |
Question 15:
What is the general solution of the following homogeneous second order differential equation?
d^2y/dx^2+ 5 dy/dx − 36.y = 0
(a) |
y = A e4.x + B e9.x |
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(b) |
y = A e-4.x + B e9.x |
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(c) |
y = A e-4.x + B e-9.x |
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(d) |
y = A e4.x + B e-9.x |
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