) For the following differential equation locate and classify its singular points on the x-axis
i)
ii)
i) The differential equation is [ x^3(x-1)y'' - 2(x-1)y' + 3xy = 0 ] We write it in standard form by dividing through by the coefficient of (y''), i.e., (x^3(x-1)): [ y'' - \frac{2(x-1)}{x^3(x-1)} y' + \frac{3x}{x^3(x-1)} y = 0 ] Simplify the coefficients: [ y'' - \frac{2}{x^3} y' + \frac{3}{x^2(x-1)} y = 0 ] Here, (P(x) = -\frac{2}{x^3}) and (Q(x) = \frac{3}{x^2(x-1)}). _____ ______ ________ _______ _________ ____ _____ ________ _______ _______ __________ ____.
________ _________ ________ ____ __________.
_________ _______ ___ _________ __________ _______ _____.
______ ________ __________ ________ ______ _______.
________ ____ _________ _________ ___ ____ ________ ______ ____ __________.
__________ _______ __________ __________ _____ ____ ______ _________ _________ ________ ___ ________.
___ _______ _____ ___ ______ __________ _____ __________.
__________ ____ _____ __________ ________ __________.
__________ _______ __________ ________ ______ __________ ______ ______.
_______ __________ _______ _________ _______ ____.
___ __________ ______ ________ _________ _________ __________ ____.
_________ ____ ________ _______ _______ ________ ______ ________ _________ _______ ____.
____ _______ ____ ______ _________ _______ _____ __________ ________ __________.
_______ ________ _________ ______ _________ ________ ______ ______ __________.
______ _______ _________ _______ __________ __________ ______ ________.
_____ ____ ________ ___ _____ ___ _______ _____ ___.
_______ ___ ____ _____ ___ ____ _____ ______ _______ ________ __________ ________.
_____ ______ ___ __________ _____ __________ _________ __________.
___ ____ ___ _______ _______ _____ ______ ___ ______ __________ _____ ______.
________ ____ _______ ________ _____ ____ ________ __________ _________.
________ _________ ___ ________ ____ ___ _________ __________ ____.
_______ ________ _____ _______ ________ ______ ___ ___ _________ ____.
______ __________ _______ __________ __________ _______.
__________ ________ ___ ____ ___ ________ ____ _______ ______.
_____ _________ _____ ____ _____ ______ ____ _____.
___ _________ ___ ________ ______ ___ ______ _______.
__________ ______ _________ ______ ______ ______.
__________ _________ _____ __________ __________ ___ _________ ______ _________ _______ _____ __________.
___ __________ _______ ______ ___ ____ ______.
_________.
Get Full Answer on WhatsApp
) Using fourth order Taylor series method with , solve the initial value problem
upto .
Using second order finite Difference method, solve the boundary value problem
Using standard five point formula, solve the Laplace equation in R where R is the square
subject to the boundary conditions
on
and
on
. Assume
.
Solve the wave equation with the initial and boundary conditions
.
with , using the explicit method upto four time levels.
) Find the displacement u(x, t) of an infinite string using the method of Fourier transform given that the string is initially at rest and that the initial displacement is f(x), .
Check whether satisfies Lipschitz condition
i) on any rectangle and
;
ii) on any strip and
;
iii) on the entire plane.
Find an approximate value of y(1.0) for the initial value problem
y = x - 2y, y(0) = 1
using Milne-Simpson’s method
with the step length . Calculate the starting value using Runge-Kutta fourth order method with the same h.