Constant or Variable Coefficients?

[ssb]

Homework Statement

$$ty' + y = \sin(t)$$

state the following:

Order of the DE
1st 2nd 3rd or n/a

Linear
Nonlinear
Not Applicable

Homogeneous
Nonhomogeneous
Not Applicable


Constant Coefficients
Variable Coefficients
Not Applicable


2. The attempt at a solution

1st,
Linear,
Nonhomogeneous

but I don't know how to distinguish between constant or variable coefficients. Is there an easy way to remember the rule here? Thanks

 

[ssb]

im pretty sure its variable because there are some y's that vary as t changes.
If this is accurate just let me know.

Also if there is a differential equation

$$y'' + y^2 = 0$$

does the fact that the y^2 make it non linear? I am hearing different arguments both ways here. Thanks! I am pretty sure that the y^2 makes it non linear by the way.

 

[HallsofIvy]

The coefficient of y' is t. Is that a constant or will it vary as t varies?

As for your second question, I don't know how you could "hear arguments both ways"! You might do well to ignore, in the future, those who "argue" that this is linear. y uis the "dependent variable" and y² is definitely a non-linear function of y! This is, without argument, a "non-linear" differential equation!