Solve the IVP (3x-y) \frac{dy}{dx} = y+2x, y(1)=1. You should give an explicit solution whenever...

Question:

Solve the IVP

{eq}(3x-y) \frac{dy}{dx} = y+2x {/eq}, y(1)=1.

You should give an explicit solution whenever it is possible.

Homogenous Differential Equations:

A homogenous differential equation is an equation in the form of {eq}\frac{dy}{dx}=f\left(\frac{y}{x}\right) .{/eq} The advantages of having homogeneous differential equation is that it can always be reduced to a separable equation by means of a algebraic substitution and manipulation.

Answer and Explanation:

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The given differential equation is a first order non linear differential equation. To keep things simpler, we'll use the notation {eq}y' {/eq} instead...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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Learn to define what a linear differential equation and a first-order linear equation are. Learn how to solve the linear differential equation. See examples.


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