Evidently you have not reviewed the definition of a linear DE:
A differential equation is linear if the unknown function and its derivatives appear to the power 1 (products of the unknown function and its derivatives are not allowed) and nonlinear otherwise.
So, the first above is linear, and the second is not.
Classify the following differential equations as linear or nonlinear:
3x' +5x=7t^2
4x^2+2x+5tx=0
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