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

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SUMMARY

The discussion centers on classifying the equation 3x + 1 = 4t and identifying the homogeneous parts of non-homogeneous differential equations. Participants clarify that 3x + 1 = 4t is not a differential equation but can be considered a zeroth-order equation. For the non-homogeneous equations 2(dx/dt) + 3x + 1 = 4t and 2sin(dx/dt) + 3x + 1 = 4t, the homogeneous parts are identified as 2(dx/dt) + 3x and 2sin(dx/dt) + 3x, respectively. The general solution for non-homogeneous linear differential equations is expressed as y = yc + yp, where yc is the homogeneous solution and yp is the particular solution.

PREREQUISITES
  • Understanding of differential equations, specifically non-homogeneous and homogeneous types.
  • Familiarity with the notation and terminology of differential calculus, such as dx/dt.
  • Knowledge of the general solution format for linear differential equations.
  • Basic algebraic manipulation skills to classify equations accurately.
NEXT STEPS
  • Study the classification of differential equations, focusing on zeroth-order and higher-order equations.
  • Learn how to derive the homogeneous solution of non-homogeneous linear differential equations.
  • Explore the method of undetermined coefficients for finding particular solutions to non-homogeneous equations.
  • Review examples of homogeneous and non-homogeneous differential equations to solidify understanding.
USEFUL FOR

Students and professionals in mathematics, particularly those studying differential equations, as well as educators looking for clarification on classifying and solving such equations.

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.
 

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