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Solve the given differential equations.$$\frac{d y}{d \theta}=\frac{2 \theta+\sec ^{2} \theta}{2 y}$$

Calculus 2 / BC

Chapter 31

Differential Equations

Section 2

Separation of Variables

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Lectures

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Solve the differential equ…

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05:23

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Solve the initial value pr…

01:25

Find the differential of e…

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Solve the given differenti…

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what we want to solve the given differential equation which states dy dx is equal to two X plus the C. Can't squared of X divided by two Y. This question is challenging our ability to solve differential equations in particular. It's challenging our ability to use our newfound method called separation of variables. To use separation of variables in this problem, we have to follow the three steps below. First. We'll isolate X and Y on either side of the equation. So push Y terms of left X term for the right. Then we'll integrate both sides of the equation because each side will have a differential B. Y R. D. X. Then we'll solve by integrating each side using integration methods which will allow us to land in our solution. So first, isolating X and Y gives to I. D. Y equals two X plus. You can't squared X. D. S. Next we're going to integrate both sides doing so, obtains integral to I. D. Y equals integral to expose Seacon square. Next, yes, just the integration methods, we have Y squared equals X squared plus 10 X plus C. The constant of integration.

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