Verify that y = e x 3 5 cos ( 2 x ) 6 5 sin ( 2 x ) is a solution of the differential...

Question:

Verify that {eq}\displaystyle y = e^{-x} - \frac{3}{5} \cos(2x) - \frac{6}{5} \sin(2x){/eq} is a solution of the differential equation {eq}\displaystyle \frac{dy}{dx} + y = -3 \cos(2x){/eq}.

Differential Equation:

A differential equation is an equation between a specified derivative on an unknown function, its values, and unknown quantities and functions. Many physical laws are most simply and naturally formulated as a differential equation. Ordinary differential equations are whose unknown functions are the function of a single variable.

Answer and Explanation: 1

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Given

The differential equation is given as {eq}\dfrac{{dy}}{{dx}} + y = - 3\cos \left( {2x} \right) {/eq}

To verify that {eq}y = {e^{ - x}} -...

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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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