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GATE 2019: Engineering Mathematics Test 4
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Question 1
The solution of the differential equation 
is where w and z are complex numbers
Question 2
A solution for the differential equation
X(t) + 2x(t) = δ(t)
With initial condition x(0–) = 0 is:
X(t) + 2x(t) = δ(t)
With initial condition x(0–) = 0 is:
Question 3
A function y(t) satisfies the following differential equation:
where d(t) is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form
where d(t) is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form
Question 4
Let 
be the solution of the differential equation 
with initial conditions 
and 
Then the value of 
is_________.
be the solution of the differential equation with initial conditions and Then the value of is_________.Question 5
Taking for granted the general solution of 
is of the form y = At2 + Bt3 for appropriate constants A and B, the value of y (2), where y is the solution that also satisfies y (1) = 2 and y′(1) = –1, is _____.
is of the form y = At2 + Bt3 for appropriate constants A and B, the value of y (2), where y is the solution that also satisfies y (1) = 2 and y′(1) = –1, is _____. Question 6
Consider the differential equation
.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is ________.
. Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is ________.
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Jun 19ESE & GATE EE
