Solve the differential equation

{eq}\frac{dy}{dx} = \frac{x - \sin y}{-1 + x \cos y} {/eq}.


Solve the differential equation

{eq}\frac{dy}{dx} = \frac{x - \sin y}{-1 + x \cos y} {/eq}.

First Order Differential Equation:

Any relation between an independent variable {eq}x {/eq} , a dependent variable {eq}y {/eq} ,and one or more of the derived functions is called an ordinary differential equation. The variables {eq}x,y {/eq} may, or may not, enter explicitly into the equation. An ordinary differential equation of first order and first degree can be written as:

{eq}\frac{dy}{dx}=f\left( x,y\right) {/eq}, where {eq}f\left( x,y\right) {/eq} is a function of two variables {eq}x,y {/eq} .

Answer and Explanation: 1

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We are given: {eq}\frac{dy}{dx} = \frac{x - \sin y}{-1 + x \cos y} {/eq}

{eq}\Rightarrow (-1 + x \cos y ) \ dy = (x - \sin y) \ dx {/eq}


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Differential Calculus: Definition & Applications


Chapter 13 / Lesson 6

This lesson explores differential calculus. It defines a differential and delves into the many uses of differential equations.

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