# Differential Equation (this should be simple, even for me, but )

In summary, the conversation discusses a modeling question involving an equation and the attempt at solving it. The problem involves finding Q(t) and the conversation discusses different methods to solve it. The final solution is found by setting all constants to zero and solving the equation for Q(t).

## Homework Statement

It's a modeling question, the question itself doesn't matter because i know how to do, but stuck on one of the equations

## Homework Equations

Q'(t)=15- 3Q(x)/800, Q(0)=2,

## The Attempt at a Solution

I'm stuck at e^(3t/800) *Q(t) = 9/109 *e^(3t/800) +c

but the answer's supposed to be
Q(t)=4000-3998e^(-3t/800)..

how? why??/

thanks

I don't understand what method you are trying to use. The typical method is: set all constants to zero, and solve this equation for Q. That is, Q'(t) + 3Q(t)/800 = 0. The answer is clearly e^(3t/800). Now multiply the entire equation by this number:

Q'(t)e^(3t/800) + 3e^(3t/800)Q(t)/800 = 15. But the stuff on the left is just (Q(t)e^(3t/800))' by the product rule. So integrate both sides, find the missing constants, and you're done.

## What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves variables, constants, and mathematical operations, and is typically used to model various phenomena in physics, engineering, and other fields.

## What is the difference between an ordinary and a partial differential equation?

An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. Ordinary differential equations are typically used to model systems that change over time, while partial differential equations are used to model systems that vary in space as well as time.

## What are some common applications of differential equations?

Differential equations are used to model a wide variety of phenomena, including population growth, chemical reactions, fluid dynamics, electrical circuits, and more. They are an important tool in many fields of science and engineering.

## What are the different methods for solving differential equations?

There are several methods for solving differential equations, including separation of variables, substitution, and using integrating factors. Other methods include power series solutions, Laplace transforms, and numerical methods such as Euler's method.

## What are some common challenges when working with differential equations?

Some common challenges when working with differential equations include determining the appropriate model to use for a given system, finding initial conditions and boundary conditions, and solving complex equations with multiple variables and constants. It can also be challenging to interpret the solutions and apply them to real-world situations.

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