# Constant or Variable Coefficients?

1. Apr 21, 2007

### ssb

1. The problem statement, all variables and given/known data

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

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 dont know how to distinguish between constant or variable coefficients. Is there an easy way to remember the rule here? Thanks

2. Apr 21, 2007

### 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? Im hearing different arguments both ways here. Thanks! Im pretty sure that the y^2 makes it non linear by the way.

Last edited: Apr 21, 2007
3. Apr 21, 2007

### HallsofIvy

Staff Emeritus
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!