Classify and Solve the following (i) (1+r) + 2ry = f(r), y(0) = 0, dy dr dy (2) dr y(5) = 2. y -r

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Classify and Solve the following
if 0 <a <1
(i) (1+x²)+ 2ry = f(r), y(0) = 0, f(r) =
dy
dx
-x, if a > 1.
fip
(2)
y(5) = 2.
dr
dy
(3) r-
+ 4y = r*y? subject to
y(1) = 1
dr
Transcribed Image Text:Classify and Solve the following if 0 <a <1 (i) (1+x²)+ 2ry = f(r), y(0) = 0, f(r) = dy dx -x, if a > 1. fip (2) y(5) = 2. dr dy (3) r- + 4y = r*y? subject to y(1) = 1 dr
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Introduction: 

A differential equation is an equation that contains the derivative of an unknown function. The derivatives of a function define the rate of change of the function at a given position. These derivatives are linked to the other functions using a differential equation. Differential equations are commonly utilized in biology, physics, engineering, and other sciences. 

 

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