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

[Freyster98]

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.

 

[LCKurtz]

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 = y_c + y_p where c_c is the general solution to the homogeneous equation and y_c is a particular solution to the NH equation.