2. Find all singular points of the following equations and determine whether each one isregular or irregular.(a) ry" + (1 – z)y' + cy = 0;(b) r²(1 – x)°y" + 2æy +4y = 0;(c) zy" +e"y +3 cos(z)y = 0;(d) y"+In |r|y +3xy = 0. (Hint: In |e| is not a polynomial, you will need to use theoriginal definition to find the singular points.)

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2. Find all singular points of the following equations and determine whether each one is regular or irregular. (a) ry" + (1 – x)y' + ry = 0; (b) r(1– x)°y" + 2ay/ + 4y = 0; (c) ry" +e*y +3 cos(x)y = 0;

2. Find all singular points of the following equations and determine whether each one is regular or irregular. (a) ry" + (1 – x)y' + ry = 0; (b) r(1– x)°y" + 2ay/ + 4y = 0; (c) ry" +e*y +3 cos(x)y = 0;

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

2. Find all singular points of the following equations and determine whether each one is
regular or irregular.
(a) ry" + (1 – z)y' + cy = 0;
(b) r²(1 – x)°y" + 2æy +4y = 0;
(c) zy" +e"y +3 cos(z)y = 0;
(d) y"+In |r|y +3xy = 0. (Hint: In |e| is not a polynomial, you will need to use the
original definition to find the singular points.)

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