11-14, verify that the function is a particular solution of the differential equation. Function 11. y sin x cos x - cos²x Differential Equation and Initial Condition 2y + y'= 2 sin 2x x (²) = 4 = 0
11-14, verify that the function is a particular solution of the differential equation. Function 11. y sin x cos x - cos²x Differential Equation and Initial Condition 2y + y'= 2 sin 2x x (²) = 4 = 0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Verifying a Particular Solution**
In Exercises 11–14, verify that the function is a particular solution of the differential equation.
**Function**
\[ y = \sin x \cos x - \cos^2 x \]
**Differential Equation and Initial Condition**
\[ 2y + y' = 2 \sin 2x - 1 \]
\[ y\left(\frac{\pi}{4}\right) = 0 \]
This problem involves verifying that the given function satisfies both the differential equation and the initial condition specified.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa1490c8-ab05-4172-8498-f7edf81cd3ae%2Fb673eae2-6137-484f-bed3-1be0425d14df%2Fil41a3_processed.png&w=3840&q=75)
Transcribed Image Text:**Verifying a Particular Solution**
In Exercises 11–14, verify that the function is a particular solution of the differential equation.
**Function**
\[ y = \sin x \cos x - \cos^2 x \]
**Differential Equation and Initial Condition**
\[ 2y + y' = 2 \sin 2x - 1 \]
\[ y\left(\frac{\pi}{4}\right) = 0 \]
This problem involves verifying that the given function satisfies both the differential equation and the initial condition specified.
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