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## Homework Statement

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.

## Homework Equations

dy/dx + 2xy = 1; y = e

^{-x2}[tex]\int[/tex](from 0 to x)e

^{t2}dt + c

_{1}e

^{-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 e

^{t2}/(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?