Search
Find a solution of the Bessel’s equation of order zero.
5. Find the series solutions of the Laguerre equation (1 ) 0
2
x y x y ny of the form
( ) ( ) 0 y x c L x n
, where
r r
n
r
n x
n r r
n
L x
2
0 ( )![( )!]
( )! ( ) ( 1)
. Hence find first four polynomials.
cotxdy=ydx=(cotx)(3e^sinx)dx
Solve [2y^2 – 4x + 5]dx = [y – 2y^2 - 4xy]dy
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)
