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Solve as differential equation.

{eq}\frac{dy}{dx} = 6 e^{2x - y}\ ; \ y(0)\ =\ 0 {/eq}.

Question:

Solve as differential equation.

{eq}\frac{dy}{dx} = 6 e^{2x - y}\ ; \ y(0)\ =\ 0 {/eq}.

The solution? of Differential Equations:

The general solution of the differential equation is the most general form that the solution can take and that doesn't take into account the initial condition.

Method of Separation of Variables to find the general solution:

Given a differential equation {eq}\frac{dy}{dx}=f(x,y) {/eq} has {eq}y=g(x,y)+C {/eq} as general solution by integrating both the sides using the separation of terms with variable {eq}x {/eq} on one side and terms with variable {eq}y {/eq} on other side.

Answer and Explanation: 1

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We have

{eq}\dfrac{dy}{dx}=6e^{2x-y}. {/eq}

By separation of variables

{eq}\implies \dfrac{dy}{dx} = \dfrac{6e^2x}{e^y}. {/eq}

{eq}\implies e^y...

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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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