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Solve the following initial value problem t \frac{dy}{dt} + 9y =6t with y(1)=9. Put the problem...

Question:

Solve the following initial value problem

{eq}t \frac{dy}{dt} + 9y =6t {/eq}

with {eq}y(1)=9 {/eq}.

Put the problem in standard form.

Then find the integrating factor and {eq}y(t) {/eq}.

linear differential equations

If the equation is in the form of {eq}\displaystyle \frac{dy}{dx}+py=Q {/eq} then,the solution to the differential equation is given by

{eq}\displaystyle y e^{\int pdx}=c+\int Q e^{\int Pdx}dx. {/eq} where c is the constant of integration and Q must contain only x terms.

Answer and Explanation: 1

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Given {eq}\displaystyle \displaystyle t \frac{dy}{dt} + 9y =6t \\ \displaystyle \frac{dy}{dt}+9\frac{y}{t}=6\\ \text{This is in the form of } \ \ ...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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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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