Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
dy/dx + 2xy = 1; y = e-x2[tex]\int[/tex](from 0 to x)et2dt + c1e-x2
The Attempt at a Solution
I have only had one class period in differential so far and we didn't get to go over much material. I imagine that one would need to differentiate y(x) with respect to x and plug into the first equation. However, I'm not quite sure what to do with the integral with respect to t. I tried to integrate it, and got et2/(2t), but evaluating that at 0 would cause an implosion. If I differentiate with respect to x, I don't think I can just treat it as a constant because it's evaluated from 0 to x. Could I please get a nudge in the right direction?