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WorksheetsEM-III
Total questions: 9
Worksheet time: 27mins
1) which of the following is the general solution to d2y /dx2 + 3dy /dx − 10y = 0?
In each case, A and B are arbitrary constants. Exactly one option must be correct)
y = Ae2x + Be−5x
y = Ae−2x + Be5x
y = Ae2x + Be5x
y = Ae−2x + Be−5x
1) Which of the following is the general solution to d2y /dt2 - 4dy/ dt +4y = 0?
In each case, A and B are arbitrary constants. Exactly one option must be correct)
y = Ae2t + Bte2t
y = Ae2t + Be−2t
y = Ae2t + Be−6t
y = Ae(−2+22)t + Be(−2−22)t
1) Which of the following are general solutions to d2x/ dt2 − 4dx/ dt + 13x = 0?
In each case, A and B are arbitrary constants.
x = Ae5t + Be−t
x = Ae(2+3i)t + Be(-2−3i)t
x = e2x(Acos3x + Bsin3x)
x = e3x(Acos2x + Bsin2x)
1) Which of the following is the general solution to d2y/dx2 + 10dy/dx + 25y = 0?
In each case, A and B are arbitrary constants. Exactly one option must be correct)
y = Ae−5x + Be−5x
y = Axe−5x + Be−5x
y = Ae5x + Be5x
y = Axe5x + Be5x
1) Consider the differential equation d2y /dx2 − 49y = 0.
Which of the following options is correct? Exactly one option must be correct)
The roots of the auxiliary equation are 0 and 7.
There is no auxiliary equation for a differential equation of this type.
The auxiliary equation has a repeated root of 7.
The roots of the auxiliary equation are 7 and −7
The general solution to d2z /dt2 + 6dz/dt + 9z = 0 is
z = Ate−3t + Be−3t. Which of the following options is correct?
As t →∞, z → A for any value of B.
The behaviour of z as t →∞ depends on the values
of A and B.
As t →∞, z → 0 for any values of A and B.
As t →∞, z →∞ for any values of A and B.
Find the general solution to d2y/dt2 − 3dy/dt − 4y = 0 satisfying y(0) = 0 and y′(0) = 5.
y = et − e−4t
y = e−t − e4t
y = e−4t − et
y = e4t − e−t
Find a solution to d2x/ dt2 + dx/dt − 2x = 0 which satisfies x(0) = 3 and does not tend to infinity (or minus infinity) as t →∞.
x = 3e−t
x = 4e−2t − et
x = 3e−2t
x = 2e−2t + e−t
1) If y = Ae3x +Be2x is a solution to d2y /dx2 − 5dy /dx + ky = 0, what is the value of k?
k = 3
k = 4
k = 5
k = 6
