Question
) For the following differential equation locate and classify its singular points on the x-axis
i)
ii)
Answer :
Word Count : 315
____ ____ __________ ________ ________.
___ ________ __________ ______ _________ __________ __________ ___ ___ _____ ________.
__________ ____ ____ _____ ___ ________ ________ _____ __________ _______ ______ ________.
_______ ____ _______ ________ _________ _____ _____ ____ ___ _______ _______ __________.
_________ ___ _____ _______ _____.
_________ ________ ______ ___ ______ __________ ________ __________ __________.
_____ ________ ________ _______ _____ ________ ______ ________ _________ _______.
__________ ____ _________ ______ _________ _____ __________ ______ ____ ______ _______.
_________ ________ __________ _________ ____.
_____ _________ ________ ________ _____ _______ ___ _______ ____ _____ _____ _______.
__________ __________ ___ ______ ________ ____ ___ _________ ____.
______ ______ _________ _____ _______ ________ _______ ________ ______ _________.
_____ _________ _____ ______ _______ ________ ____ ________ ___ _________ ________ ___.
_______ _________ ______ ________ ____ ______ _____ ___ ______ ___ _______.
___ ____ _______ ____ _____ ___ ________ ______ _______ _____ _____.
________ ___ _______ ____ _________ ____ ________ ____ ____ ______ _______ _______.
_______ _____ ___ _________ ______ ___ ______.
_______ _________ ____ ____ ___ ______ ___ ___.
____ _______ _________ _______ ___.
_____ ________ ________ __________ __________ _________ ____ ______ ___ ______ ____.
____ _________ ____ ________ _________ _________ ______ _______ _______ ___.
Skip in 10
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)}). Singular points occur where the coefficients are not analytic, i.e., where (x^3(x-1) = 0), giving (x = 0) and (x = 1). * At (x = 0): [ (x-0)P(x) = x\left(-\frac{2}{x^3}\right) = -\frac{2}{x^2} \quad \text{not analytic}, ] [ (x-0)^2 Q(x) = x^2 \cdot \frac{3}{x^2(x-1)}
_____ ________ __________ __________ ____ __________ _________ ______ ___ ________.____ ____ __________ ________ ________.
___ ________ __________ ______ _________ __________ __________ ___ ___ _____ ________.
__________ ____ ____ _____ ___ ________ ________ _____ __________ _______ ______ ________.
_______ ____ _______ ________ _________ _____ _____ ____ ___ _______ _______ __________.
_________ ___ _____ _______ _____.
_________ ________ ______ ___ ______ __________ ________ __________ __________.
_____ ________ ________ _______ _____ ________ ______ ________ _________ _______.
__________ ____ _________ ______ _________ _____ __________ ______ ____ ______ _______.
_________ ________ __________ _________ ____.
_____ _________ ________ ________ _____ _______ ___ _______ ____ _____ _____ _______.
__________ __________ ___ ______ ________ ____ ___ _________ ____.
______ ______ _________ _____ _______ ________ _______ ________ ______ _________.
_____ _________ _____ ______ _______ ________ ____ ________ ___ _________ ________ ___.
_______ _________ ______ ________ ____ ______ _____ ___ ______ ___ _______.
___ ____ _______ ____ _____ ___ ________ ______ _______ _____ _____.
________ ___ _______ ____ _________ ____ ________ ____ ____ ______ _______ _______.
_______ _____ ___ _________ ______ ___ ______.
_______ _________ ____ ____ ___ ______ ___ ___.
____ _______ _________ _______ ___.
_____ ________ ________ __________ __________ _________ ____ ______ ___ ______ ____.
____ _________ ____ ________ _________ _________ ______ _______ _______ ___.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.
Related Questions
Using second order finite Difference method, solve the boundary value problem
Check whether satisfies Lipschitz condition
i) on any rectangle and
;
ii) on any strip and
;
iii) on the entire plane.
Solve the wave equation with the initial and boundary conditions
.
with , using the explicit method upto four time levels.
Show that
Find an approximate value of y(1.0) for the initial value problem
using the multiple method
with step length . Calculate the starting values using Runge-Kutta second order method with the same h.
Find the Laplace transform of
Solve the following IBVP using the Laplace transform technique: