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Find the solution of the initial value problem:

$$\frac{dx}{dt} - 3x = t + 2,\ x(0) = -1 $$

Question:

Find the solution of the initial value problem:

$$\frac{dx}{dt} - 3x = t + 2,\ x(0) = -1 $$

Initial Value Problem:

An initial value problem is the consists of,

(1) The first order differential equation of the form {eq}f\left( {x,y} \right) = y' {/eq}. Where, {eq}f\left( {x,y} \right) {/eq} is the function of {eq}x {/eq} and {eq}y {/eq}, and {eq}y' {/eq} is the derivative of {eq}y {/eq}.

(2) An initial condition of the form {eq}y\left( a \right) = b {/eq}.

Answer and Explanation: 1

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Given

The initial value problem is given as {eq}\dfrac{{dx}}{{dt}} - 3x = t + 2,x\left( 0 \right) = - 1 {/eq}.

The differential equation is of the...

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Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.


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