Differential Equations Answers

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 + e^x/2

1. 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.