# Solving Inhomogeneous equation

• darkspym7
In summary, to solve the inhomogeneous equation y'' + 4y = 4 with y(0)=0 and y'(0)=0, the constant function y(t)=1 is a particular solution that must be added to the general solution of the homogeneous equation. This can be found by setting y(t) = A, where A is a constant, and solving for A.
darkspym7

## Homework Statement

Solve the inhomogeneous equation y'' + 4y = 4 with y(0)=0 and y'(0)=0.

## The Attempt at a Solution

let Y(t) = A, A being some constant
Y'(t) = 0
Y''(t) = 0

Y''(t)+4Y(t)=4
=> 4Y(t)=4
=> 4A=4
=> A=1
=> y(t)=1
But y(0)=0, so that cannot be correct.

Any tips?

It looks like y is not a constant function; but a variable function that satisfies y'' + 4y = 4 with y(0)=0 and y'(0)=0.

EnumaElish said:
It looks like y is not a constant function; but a variable function that satisfies y'' + 4y = 4 with y(0)=0 and y'(0)=0.

Yeah, I saw that, but how could I go about solving it if the right hand side is constant?

The function $y(t)=1$ is a particular solution. You have to add this to the general solution of the homogeneous equation. Can you find it?

## 1. What is an inhomogeneous equation?

An inhomogeneous equation is a mathematical equation where the terms on one side are not equal to those on the other side. This means that the equation does not have a solution that satisfies the equation for all values of the variables.

## 2. How is an inhomogeneous equation solved?

An inhomogeneous equation can be solved by using various techniques such as substitution, elimination, or using matrices. The goal is to rearrange the equation into a simpler form that can be easily solved. The solution to the equation will depend on the specific method used.

## 3. What is the difference between a homogeneous and an inhomogeneous equation?

A homogeneous equation is one where all the terms on both sides are of the same degree. This means that the equation has a solution that satisfies the equation for all values of the variables. On the other hand, an inhomogeneous equation has terms of different degrees and does not have a solution that satisfies the equation for all values of the variables.

## 4. Can an inhomogeneous equation have multiple solutions?

Yes, an inhomogeneous equation can have multiple solutions. This is because there are different methods that can be used to solve the equation, and each method may result in a different solution. Additionally, some inhomogeneous equations may have infinite solutions.

## 5. In what fields of science are inhomogeneous equations commonly used?

Inhomogeneous equations are commonly used in fields such as physics, engineering, and economics. They are used to model real-world systems and phenomena that involve multiple variables and non-uniform conditions. Solving inhomogeneous equations allows scientists to make predictions and analyze the behavior of these systems.

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