Determining weather these functions satisfy the differential equation: ...?

[math?]

This is the differential equation:
y' + xy = x
These are the two functions:
y_1(x) = e^[-(x^2)/(2)]
y_2(x) = 1 + Ce^[-(x^2)/(2)]

We need to know if these two functions (individually) satisfy the differential equation. Show your work. Thank you!

[cidyah]

y=e^(-x^2/2)
y'=e^(-x^2/2) (-2x/2)
y'=-xe^(-x^2/2)
y'+xy = -xe^(-x^2/2)+xe^(-x^2/2) = 0
Doesn't satisfy.

y=1+Ce^(-x^2/2)
y'=-Cxe^(-x^2/2)
y'+xy = -Cxe^(-x^2/2)+x(1+Ce^(-x^2/2)
y'+xy =-Cxe^(-x^2/2)+x+xCe^(-x^2/2) = x
y'+xy=x
satisfies