Classifying DiffEq: 3x+1=4t, Identify Homogeneous Parts

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In summary: The homogeneous part is the solution to the homogeneous equation, so in the first case it is 2(dx/dt)+3x and in the second it is 2sin(dx/dt)+3x. In summary, the first equation can be considered zeroth order and the homogeneous part of both equations is 2(dx/dt)+3x.
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Freyster98
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I need to classify a bunch of differential equations and this one has me stuck...

3x+1=4t

Would this be zeroth order? Or should I just call it a quadratic equation?

Also, I need to identify the homogeneous parts of these equations. I know what a homegeneous differential equation is, but how would I identify the homogeneous part of a non-homogeneous equation?

2(dx/dt) +3x+1=4t

Would the homogeneous part just be: 2(dx/dt)+3x?

2sin(dx/dt)+3x+1=4t

answer: 2sin(dx/dt)+3x?

I'm stuck, any help would be a huge help.
 
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Freyster98 said:
I need to classify a bunch of differential equations and this one has me stuck...

3x+1=4t

Would this be zeroth order? Or should I just call it a quadratic equation?

I wouldn't call it a differential equation but I suppose you could consider it a zeroth order. I certainly wouldn't call it a quadratic.
Also, I need to identify the homogeneous parts of these equations. I know what a homegeneous differential equation is, but how would I identify the homogeneous part of a non-homogeneous equation?

2(dx/dt) +3x+1=4t

Would the homogeneous part just be: 2(dx/dt)+3x?

2sin(dx/dt)+3x+1=4t

answer: 2sin(dx/dt)+3x?

I'm stuck, any help would be a huge help.

I am guessing you are talking about the homogeneous part of the solution. The general solution of a NH linear DE is y = yc + yp where cc is the general solution to the homogeneous equation and yc is a particular solution to the NH equation.
 

Related to Classifying DiffEq: 3x+1=4t, Identify Homogeneous Parts

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model how a system changes over time.

2. What is the difference between linear and nonlinear differential equations?

A linear differential equation is one in which the dependent variable and its derivatives appear only in a linear form, whereas a nonlinear differential equation contains terms that are not linear. This means that the solutions to nonlinear differential equations can be more complex and difficult to find than those to linear ones.

3. What does it mean for a differential equation to be homogeneous?

A homogeneous differential equation is one in which all terms can be written as a multiple of the dependent variable and its derivatives. This means that the equation can be simplified by dividing out the dependent variable and its derivatives, making it easier to solve.

4. How do you identify the homogeneous parts of a differential equation?

To identify the homogeneous parts of a differential equation, you need to rewrite the equation so that all terms are grouped together on one side. The terms that are multiples of the dependent variable and its derivatives are the homogeneous parts.

5. How can you solve a homogeneous differential equation?

To solve a homogeneous differential equation, you can use the method of separation of variables or find an integrating factor. You can also use substitution or transformation techniques to reduce the equation to a simpler form. It is important to check your solution by plugging it back into the original equation to ensure it satisfies all of the conditions.

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