dx dt = tan x
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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Graph the phase portrait of the system..
![The image displays a differential equation, which is expressed mathematically as follows:
\[ \frac{dx}{dt} = \tan x \]
Explanation:
- \(\frac{dx}{dt}\) represents the derivative of \(x\) with respect to \(t\). This notation is commonly used in calculus to indicate how \(x\) changes as \(t\) changes.
- \(\tan x\) represents the tangent function of \(x\). The tangent function is one of the basic trigonometric functions and is defined as the ratio of the sine of an angle to the cosine of the same angle, i.e., \(\tan x = \frac{\sin x}{\cos x}\).
This equation suggests that the rate of change of \(x\) with respect to \(t\) is equal to the tangent of \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa59c8a62-6d27-4c14-9dc5-c4241c4a7fe0%2Fd8030d4a-a0c4-4343-a3bb-1c2e3d745b34%2Fca8o97c_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a differential equation, which is expressed mathematically as follows:
\[ \frac{dx}{dt} = \tan x \]
Explanation:
- \(\frac{dx}{dt}\) represents the derivative of \(x\) with respect to \(t\). This notation is commonly used in calculus to indicate how \(x\) changes as \(t\) changes.
- \(\tan x\) represents the tangent function of \(x\). The tangent function is one of the basic trigonometric functions and is defined as the ratio of the sine of an angle to the cosine of the same angle, i.e., \(\tan x = \frac{\sin x}{\cos x}\).
This equation suggests that the rate of change of \(x\) with respect to \(t\) is equal to the tangent of \(x\).
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