(1) Use series to find the solution of the differential equation (x²-1)y" + 3xy + xy = 0 with y(0) = 4, y' (0) = 6.
(1) Use series to find the solution of the differential equation (x²-1)y" + 3xy + xy = 0 with y(0) = 4, y' (0) = 6.
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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Transcribed Image Text:(1) Use series to find the solution of the differential equation (x²-1)y"+3xy + xy = 0
with y(0) = 4, y' (0) = 6.
(2) Show that L{(1 + ²)²}=
(3) For the differential equation
4(s² - 4s+2)
s(8-2)(8-4)
(a) Separation of variables;
(b) Linear equations method;
do the following:
(a) Show that x = 0 is a regular singular point.
(b) Find the indicial equation and the indicial roots of it.
(c) Use the Frobenius method to find two series solutions of the equation:
(4) Solve the first order differential equation y - 3y = 0 with y(0) = 1 using the
following methods:
(c) Power series method; and
(d) Laplace Transform Method.
y
4xy + +y=0
2
(5) Use the Laplace Transform Method to solve the linear equation y" -y - 2y = 4t²
with initial conditions y(0) = 1 y' (0) = 4
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