Solve the first order differential equation 3xy'-y=x^{-1}


Solve the first order differential equation

{eq}3xy'-y=x^{-1} {/eq}

First Order Linear Differential Equation :

A first-order linear differential equation of the form {eq}y'(x)+p(x)y(x)=q(x) {/eq} has the integrating factor (IF) {eq}e^{\int p(x)dx} {/eq} and its solution is given by {eq}y.IF=\int q(x).IF \ dx+C, {/eq} where C is constant of integration. We can reduce the given equation into standard form and find its solution.

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The given equation is {eq}\displaystyle 3xy'-y=x^{-1}\\ \displaystyle \Rightarrow \frac{dy}{dx} - \frac{1}{3x}y = \frac{1}{3x^2}\\ {/eq}

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First-Order Linear Differential Equations


Chapter 16 / Lesson 3

In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.

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