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Find constants $ A $ and $ B $ such that the function $ y = A \sin x + B \cos x $ satisfies the differential equation $ y" + y' - 2y = \sin x. $
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01:30
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Ethan T.
September 30, 2022
where did you get the 3
Campbell University
Baylor University
University of Nottingham
Boston College
Lectures
04:40
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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It's Claire's, the one you married here. So we have. Why is equal to a sign minus B sign. We're gonna differentiate. Get a co sign minus B Sign we differentiate again. We got negative A sign minus b co sign. So when we substitute, we get the second derivative. Thus, the first derivative minus two. Why? It's equal to sign the nine week put negative, eh? Sine x minus b co sign waas a co sign minus b sign minus two times a sign must be co sign and it's equal to sign when we simplify and we get okay minus three b. No sign. Plus negative three A minus B I'm sign, which is equal to zero. I'm school sign. It was one time sign. No, we look at both sides. We have the equations, which is a minus three b equals Sarah Negative. Three a minus B people's one. So we're gonna find be in a So you get three a my next 93 My next three a minus b equals one. We get b is equal to negative one time and A is equal to negative. Three time
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