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Determine if the following statements are true or false. O TRUE O FALSE The differential equation y = sin x cos y + cos x sin y is separable. O TRUE O FALSE The differential equation (xy² + e®)dx + (y³/3+ e²)dy =0 is exact. TRUE O FALSE The differential equation xy + cos(x)y= –2e¬² is linear. O TRUE O FALSE The initial value problem below is guaranteed to have a unique solution on a rectangle containing the initial value. cost y(0) = -1 y +2°

Determine if the following statements are true or false. O TRUE O FALSE The differential equation y = sin x cos y + cos x sin y is separable. O TRUE O FALSE The differential equation (xy² + e®)dx + (y³/3+ e²)dy =0 is exact. TRUE O FALSE The differential equation xy + cos(x)y= –2e¬² is linear. O TRUE O FALSE The initial value problem below is guaranteed to have a unique solution on a rectangle containing the initial value. cost y(0) = -1 y +2°

Advanced Engineering Mathematics
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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1. Determine if the following statements are true or false. O TRUE O FALSE The differential equation y' = sin x cos y + cos x sin y is separable. O TRUE O FALSE The differential equation (xy² + e")dx + (y³/3+e)dy = 0 is exact. TRUE The differential equation xy + cos(x)y= -2e¬ is linear. FALSE O TRUE FALSE The initial value problem below is guaranteed to have a unique solution on a rectangle containing the initial value. cost y = y + 2' y(0) = –1
Transcribed Image Text:1. Determine if the following statements are true or false. O TRUE O FALSE The differential equation y' = sin x cos y + cos x sin y is separable. O TRUE O FALSE The differential equation (xy² + e")dx + (y³/3+e)dy = 0 is exact. TRUE The differential equation xy + cos(x)y= -2e¬ is linear. FALSE O TRUE FALSE The initial value problem below is guaranteed to have a unique solution on a rectangle containing the initial value. cost y = y + 2' y(0) = –1
Expert Solution
Step 1

(1) 

(a) Given statement, "The differential equation y'=sinxcosy+cosxsiny is separable" is false.

(b) Given statement, "The differential equation xy2+eydx+y33+exdy=0 is exact" is false.

Because, here M=xy2+ey and N=y33+ex

And ∂M∂y≠∂N∂x

So the statement, "The differential equation xy2+eydx+y33+exdy=0 is exact" is false.

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