# Solve the differential equation {eq}y' + 2y = e^{-2x} {/eq}

## Question:

Solve the differential equation {eq}y' + 2y = e^{-2x} {/eq}

## Linear Differential Equations:

The order of the largest derivative in the differential equation determines the order of the differential equation, it is the same for the ordinary and partial differential equation. In order to recognize if an equation is linear, we can take into account three fundamental aspects.

#### Fundamental aspects

• The dependent variable and all its derivatives are of degree 1
• There are no products of the dependent variables.
• There are no transcendent functions such as trigonometric or logarithmic.

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Given:

$$y'+2y=e^{-2x}$$

The given differential equation is linear. First, we compute the integration factor:

$$I.F.=e^{\int 2dx}=e^{2x}$$

Sub...