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ESE 2020: Engg. Mathematics Quiz 5
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Question 1
Which one of the following statements is true about the differential equation given below?
(xy3 + y)dx + 2(x2y2 + x + y4)dy = 0
Question 2
The maximum slope of the curve
y = –x3 + 3x2 + 2x – 27 is
Question 3
The solution to the partial differential equation 
subjected to the initial condition U(x,y) = 4e-2x is
subjected to the initial condition U(x,y) = 4e-2x isQuestion 4
F(x) = x(x-3)e-x/2defined in the range [-3,4] , mean value theorems applicable to the function are
Question 5
Consider a curve described by f(x) = 2x3 – 3x2 – 36x + 10. Minimum of slope for the given curve occurs at what value of x.
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
is initially at rest. For input x(t) = 2u(t), the output y(t) is Question 7
Solution of the differential equation x
= y{log(y) – log(x)+1} is
= y{log(y) – log(x)+1} is Question 8
The PDE given below is commonly known as:
Question 9
The solution of differential equation 
is
isQuestion 10
Let a causal LTI system be characterized by the following differential equation, with initial rest condition
Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)
Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)
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May 29ESE & GATE CE
