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True or False: (1) There is a solution of y' = 24, which is decreasing when x < 0. (a) m1 2

True or False: (1) There is a solution of y' = 24, which is decreasing when x < 0. (a) m1 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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**True or False:** 1. There is a solution of \( y' = \frac{x^2 + 4}{e^{x-y}} \) which is decreasing when \( x \leq 0 \). 2. The equation \( y' = y(x^2 - 4) \) has three equilibrium solutions. 3. When we draw the slope field of \( y' = \sin(x^2)(x+y+2)(x^2-4) \), the arrows on the \( y \)-axis all have slope 0. 4. All solutions of \( y' = x(y^2 + 4) \) are increasing functions.
Transcribed Image Text:**True or False:** 1. There is a solution of \( y' = \frac{x^2 + 4}{e^{x-y}} \) which is decreasing when \( x \leq 0 \). 2. The equation \( y' = y(x^2 - 4) \) has three equilibrium solutions. 3. When we draw the slope field of \( y' = \sin(x^2)(x+y+2)(x^2-4) \), the arrows on the \( y \)-axis all have slope 0. 4. All solutions of \( y' = x(y^2 + 4) \) are increasing functions.
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