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1. An object of mass 20 kg is pushed on a floor with a force of 40sin 2t N. Given that the
frictional force is 20 times the velocity and the object starts from rest, determine the
velocity of the object as a function of time.
2. Consider an LCR circuit with L = 0.1 H, C = 0.01 F and R = 3.0. Determine the
electric current in the circuit, given that at t = 0, the charge in the circuit is zero and the
current is 2 A.
Using the Frobenius method, solve the following ODE:
x²y"+4xy'+(x²+2)y=0
Determine all the first and second order partial derivatives for the function:
u(x,t)=Ce^(1-n²π²)t sin (nπx)
Reduce the equation to a set of ODDE. using separation of variable
(del)²A+[k²+f(p)+1/p² g(B)+h(z)]A =0
dy/dx+2y/x=sinx/x²
(d^2+dd'+d'+1) =5e^x
(3D^2-2D^2+D-1)z=4e^(x+y).cos(x+y)
y'' − y' + 1/4 y = 8 + ex/2
- ysin 2x dx-dy-y^2dy-cos^2xdy=0
In a chemical manufacturing plant, a certain type of chemical B is produced
through reactions in chemical A. Through observation the officers on duty have
noted that the rate of conversion from chemical A to B is proportion to the
amount of chemical A present at any time, further investigation has revealed
that 10% amount has been converted in first five minutes.
a) The plant manager wishes to know the percentage of chemical A that will
be converted in 20 minutes.
b) The plant manager wishes to know the time it will take to convert 60
minutes of chemical A.
