Differential equation with only the trivial solution

[Bipolarity]

Homework Statement

Find a differential equation with its only (complex-valued) solution being y=0

Homework Equations

The Attempt at a Solution

I believe that there is no DE having only y=0 as its solution, but frankly I am not sure if this is the case. I would like to know whether or not this is true, so that I know in which direction I can begin working my proof (or at least a hint is appreciated).

Also, something (in my mind) tells me this problem may have some connection with Wronskian matrices, but I have no clue really.

EDIT: I tried playing with some random diff Eqs, it seems that there are in fact trivial things like y+y'-y'=0, but this type of answer seems to be trivial to be of substance. Is there a DE that does not reduce to a trivial y=0?

Thanks!

BiP

 

[haruspex]

One approach is to think of a function of y' that cannot be zero, f(y') say, then write f(y')y = 0.

 

[Dick]

One approach is to think of a function of y' that cannot be zero, f(y') say, then write f(y')y = 0.

Well, f(y')=1 works. Still seems like kind of a cheat. Notice they also said complex valued. So something like f(y')=1+(y')^2 won't work either. Not to say you can't cook one up. Like f(y')=(1+(y')(y'*)). I'm just wondering if there is something nontrivial here.

 

[haruspex]

I was thinking of e^y'y=0

 

[Bipolarity]

I was thinking of e^y'y=0

Good work! And thanks!

BiP