Expected value of 2 Normal variables

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What would be the expected value of: $$ E[e^{aX-Y}]\\$$ X, Y~Normal(mu, sigma^2)

Right now I have:

$$ e^{(aE[X]-E[Y]+1/2[a^2Var[X]-Var[Y]-2aCov(X,Y)])} $$

Is it correct?