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Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

1. dy/dx + xy = e^-x
2. dy/dx + xy = 0
3. dy/dx + xy = e^-y
4. dy/dx + e^-y = 0

Correct answer: dy/dx + xy = e^-x

Solution

This equation is linear because it can be expressed in the form of a linear combination of the dependent variable and its derivatives, and it is non-homogeneous due to the presence of the term e^-x on the right side, which is not a function of y.

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