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Solve the differential equation. \sin \theta \frac{dr}{d \theta} + (\cos \theta)r = \tan...

Question:

Solve the differential equation.

{eq}\sin \theta \frac{dr}{d \theta} + (\cos \theta)r = \tan \theta, 0 < \theta < \frac{\pi}{2} {/eq}

r = _____ (Use C as the arbitrary constant.)

Simplification of Differential Equation:

An equation with derivative term is called differential equation.

Equation of form {eq}\displaystyle \frac{dr}{d\theta }+Pr=Q {/eq} is called linear differential equation.

Where, P and Q are constant or function of {eq}\displaystyle \theta {/eq}.

It's solution is

{eq}\displaystyle r\left(I.F\right)=\int \:Q\left(I.F\right)d\theta+C {/eq} with integrating factor {eq}\displaystyle I.F=e^{\int \:P\:d\theta } {/eq}.

Answer and Explanation: 1

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Given differential equation:

{eq}\displaystyle \sin \theta \frac{dr}{d \theta} + (\cos \theta)r = \tan \theta {/eq}

Divide both side by...

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Integrating Factor: Method & Example

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Chapter 12 / Lesson 6
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Learn how to find integrating factors. Review the integrating factor method and formula to solve linear first- and second-order differential equations with examples.


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