# Solve the initial value problem dy/dt - y = 8e^t + 40e^(9t) with y(0) = 5.

## Question:

Solve the initial value problem {eq}\frac{\mathrm{d} y}{\mathrm{d} t} - y = 8e^t + 40e^{9t} {/eq} with {eq}y(0) = 5 {/eq}.

## Initial Value Problem:

An initial value problem is a differential equation given with specified initial conditions. To solve the initial value problem, we take the following steps

1) Integrate the differential equation to get a general solution

2) Use the given initial condition to find the particular solution of the differential equation

## Answer and Explanation:

The given differential equation is a linear first order differential equation, we use the method of integrating factor to solve this differential...

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