Problem 3 We assume y₁(x) solve the following differential equation: y" + P(x)y' + Q(x)y = 0, then we can find another solution y₂(x), using the following formula: e Y2(T) = Y1(T) | ² -dr. SP(z)dz y? We now consider to find the general solution to the equation y" - 4y + 4y = 0. (2.1) Show that y₁(x) = e²¹ is a solution of (1). (2.2) Using the formula we have above, find y2(x)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 33CR
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Problem 3 We assume y₁(x) solve the following differential equation:
y" + P(x)y' + Q(x)y = 0,
then we can find another solution y₂(x), using the following formula:
SP(x)dr
y²
We now consider to find the general solution to the equation
y" - 4y + 4y = 0.
e
Y₂(T) = Y₁(x) [² -d.x.
(2.1) Show that y₁(x) = e² is a solution of (1).
(2.2) Using the formula we have above, find y2(x)
Transcribed Image Text:Problem 3 We assume y₁(x) solve the following differential equation: y" + P(x)y' + Q(x)y = 0, then we can find another solution y₂(x), using the following formula: SP(x)dr y² We now consider to find the general solution to the equation y" - 4y + 4y = 0. e Y₂(T) = Y₁(x) [² -d.x. (2.1) Show that y₁(x) = e² is a solution of (1). (2.2) Using the formula we have above, find y2(x)
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9780321964038
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GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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