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Solve the differential equation. (Use C for any needed constant.) \\ 4\frac{dy}{d\theta} = \frac...

Question:

Solve the differential equation. (Use C for any needed constant.)

$$4\frac{dy}{d\theta} = \frac {e^y \sin ^2\theta}{y \sec \theta}$$

Integration using by parts and variable separable methods

To solve the given integral equation we have to use integration by parts method and variable separable method.

Integration by parts .

Let u and {eq}v^{\prime} {/eq} be two functions in t then

{eq}\int u v^{\prime} dt = u v - \int u ^{\prime} v dt + C {/eq}

Variable separable method.

If the differential equation is in the form {eq}\frac { dy}{dx } = F(x) \ G(y) {/eq} Where F and G are functions in x and y respectively .

Then we can convert the given d.e in the form {eq}\frac { dy}{G(y) } = F(x) \ dx \\ => \int \frac { dy}{G(y) } = \int F(x) \ dx {/eq}.

Answer and Explanation: 1

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Given integral is

{eq}\begin{align*} & 4\frac{dy}{d\theta} = \frac {e^y \sin ^2\theta}{y \sec \theta}\\ & => 4 y e ^{-y} \ dy =\frac { \sin...

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Integration Problems in Calculus: Solutions & Examples

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Chapter 13 / Lesson 13
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Learn what integration problems are. Discover how to find integration sums and how to solve integral calculus problems using calculus example problems.


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