# Are solultions of D.E. a Vector Space?

1. Apr 21, 2006

### coldturkey

----------------------

Let V be the solutions to the differential equation:

$a_{1}y' + a_{0} = x^2 + e^x$

Decide using the properties of pointwise addition and scalar multiplication if V is a vector space or not.

---------------------

Ok im having real trouble with this question. I can prove is something is a vector space aslong as I know what im trying to proove.

To solve this question do I need to find or make up y? Or am I just assuming V = (a0, a1) and need to prove something like
$$(a1 + b1)y' + (a0+b0) = x^2 + e^x + b1y' + b0$$