Non exact differential equation, initial value problem

In summary, a non exact differential equation is a type of differential equation with coefficients that cannot be expressed as a single variable function. It is more difficult to solve than an exact differential equation. An initial value problem is a differential equation with specified values at a starting point, making it easier to find a unique solution. To solve a non exact differential equation, an integrating factor or numerical methods can be used. The difference between exact and non exact differential equations lies in the form of their coefficients. Initial value problems are important in solving differential equations because they provide a starting point and make the solution unique.
  • #1
Cocoleia
295
4

Homework Statement


I am trying to solve the following:
y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38

Homework Equations

The Attempt at a Solution


upload_2016-12-8_9-34-25.png

upload_2016-12-8_9-34-52.png


The right answer is:
y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x

I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?
 
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  • #2
When computing ##y'## at the top of the second you are missing the constant ##1## coming from ##(x)'##=1.
 

What is a non exact differential equation?

A non exact differential equation is a type of differential equation where the coefficients of the variables are not exact differentials. This means that they cannot be expressed as the derivative of a single variable function. These equations are typically more difficult to solve than exact differential equations.

What is an initial value problem?

An initial value problem is a type of differential equation where the values of the variables are specified at a certain initial point. The goal is to find the solution to the equation that satisfies these initial conditions. In other words, the initial value problem provides a starting point for solving the differential equation.

How do you solve a non exact differential equation?

One method for solving a non exact differential equation is by using an integrating factor. This involves multiplying the entire equation by a specific function that will make the coefficients exact and allow for the equation to be solved. Another method is by using a series expansion or numerical methods.

What is the difference between an exact and non exact differential equation?

The main difference between an exact and non exact differential equation is that the coefficients of the variables in an exact differential equation can be expressed as the derivative of a single variable function. In a non exact differential equation, this is not possible and the equation must be solved using other methods.

Why are initial value problems important in solving differential equations?

Initial value problems are important in solving differential equations because they provide a starting point for finding the solution. Without these initial conditions, the solution to the differential equation would have an infinite number of possibilities. The initial values help to narrow down the solution and make it unique.

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