# 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

Become a Study.com member to unlock this answer!

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...

See full answer below.