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Solve the following ODE. cosy + (1 + e^{-x}) siny\frac{dy}{dx} = 0,\; given\; that\; y = \pi/4 \;...

Question:

Solve the following ODE.

{eq}cosy + (1 + e^{-x}) siny\frac{dy}{dx} = 0,\; given\; that\; y = \pi/4 \; when\; x = 0 {/eq}

Ordinary Differential Equation:


An ordinary differential equation has independent and dependent variables and differentiation of dependent variables with respect to the independent variable. To solve the given differential equation, use the variable separable method and then integrate.

Answer and Explanation: 1

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Given

  • The differential equation is {eq}\cos y + \left( {1 + {e^{ - x}}} \right)\sin y\dfrac{{dy}}{{dx}} = 0 {/eq}, initial condition is...

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Separable Differential Equation: Definition & Examples

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Chapter 16 / Lesson 1
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Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.


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