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Solve the given differential equations.$$d y=k(20+y) d t$$

Calculus 2 / BC

Chapter 31

Differential Equations

Section 2

Separation of Variables

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Determine the general solu…

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Solve the given differenti…

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Solve the differential equ…

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Find the values of $k$ for…

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Uh huh. We want to solve the given differential equation dy is equal to K terms 20 plus Y dx. This question is challenging our understanding of differential equations and how to solve them. In particular, it's challenging our ability to use our newfound method of solving known as separation of variables. The separation of variables methods has three steps to complete that. I've listed below. They are first to isolate X and Y. So we put y terms on the left side of the equation. Extremes in the right second. We integrate both sides of the equation because both sides of the equation will have a differential dy dx third. We will solve such that we have a given solution. So let's go ahead and do step one. This gives 1/20 plus Y D Y equals K D X. Okay. Can be on either side of the equation. So I kept it on the right. Arbitrarily next integrating now solving these intervals using integration methods, gifts Ln 20 plus Y equals K X plus C. The constant of integration.

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