By using the definition of singularity and aslo definition poles and essential singular point.i was solved this question.
f(z) = 37" sin(-), n ezt If there are singular points, classify them. If there are...
(Singular Points) (a) Classify the singular points of the differential equation (22 – 1)?y" + (x + 1)y' – y = 0. (b) Determine the indicial equation for the regular singular point(s) found in part (a). Also find the corresponding exponents of the singularity for those points.
III. Find all singular points and classify them. (x2 -9)y" + (x – 3)y' + (x + 3)y = 0.
III. Find all singular points and classify them. (x2 -9)y" + (x – 3)y' + (x + 3)y = 0.
sin z-tanz Find and classify all singularities of the function f(z) = 2
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
(16 points total) Let g(t) = (2-sin t)2, (a) (4 points) Find a rational function f(z) such that f(e)) 5. t (Hint: Let z = eit and express cost and sint in terms of z) b) (3 points) Find and classify all the isolated singularities of the function f(2) in part We were unable to transcribe this image
7 Find all stationary points of the given system and classify them. d.r dt dy sin(r + y) dt
10. Classify the behavior of f() = * at z = 20. If it is a zero or pole, give its order.
please explain and show all work differential equations 11. Find and classify the singular points of the differential equation x? (x2 - 4)y" - (x² - 4)y' + xy = 0 (5 points)