A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0, when the forcing function is x(t), and the initial condition is y(0). If one wishes to modify the system so that the solution becomes –2y(t) for t > 0, we need to(GATE 2013 || EC || MCQ ||1 MARK)

change the initial condition to –2y(0) and the forcing function to –2x(t)

change the initial condition to –y(0) and the forcing function to 2x(t)

change the initial condition to 2y(0) and the forcing function to –x(t)

change the initial condition to and the forcing function to

GATE EC|| MATHEMATICS || TRANSFORM THEORY || PYQs (2000-2025)

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Question 1

(GATE 2018 || EC ||1 MARK)

–0.21

Question 2

If the characteristic equation of the differential equation

d²y/dx² + 2αdy/dx + y=0 has two equal roots, then the values of α are ________.

± 1
0,0
±j
± 1/2

Question 3

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0, when the forcing function is x(t), and the initial condition is y(0). If one wishes to modify the system so that the solution becomes –2y(t) for t > 0, we need to

(GATE 2013 || EC || MCQ ||1 MARK)

change the initial condition to –y(0) and the forcing function to 2x(t)
change the initial condition to 2y(0) and the forcing function to –x(t)
change the initial condition to and the forcing function to
change the initial condition to –2y(0) and the forcing function to –2x(t)

Question 4

Consider the differential equation d²y(t)/dt²+ 2dy(t)/dt+ y(t)=δ(t) with y(t)∣_t=0= −2 and dy/dt∣_t=0= 0. The numerical value of dy/dt∣_t=0

is ________.

–2
–1
0
1

Question 5

A solution of the differential equation x′(t)+2x(t)=δ(t), with the initial condition x(0−)=0, is __________.

(GATE 2006 || EC || MCQ ||1 MARK)

e^–2tu(t)
e^2tu(t)
e^–tu(t)
e^tu(t)

Question 6

A system described by the following differential equation is initially at rest. For input x(t) = 2u(t), the output y(t) is

(GATE 2004 || EC || MCQ ||1 MARK)

(1 – 2e^–t + e^–2t) u(t)
(1 + 2e^–t – e^–2t) u(t)
(0.5 + e^–t + 1.5e^–2t) u(t)
(0.5 + 2e^–t + 2e^–2t) u(t)

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