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🗝️ Key Takeaways ...

The order of a differential equation is the highest derivative of the dependent variable that appears. Only derivatives, not exponents, affect the order.
A linear term includes exactly one occurrence of the dependent variable or one of its derivatives, raised to the first power and not inside another function. Coefficients do not affect linearity.
A nonlinear term involves a product, quotient, exponent, or function of the dependent variable or its derivatives.
A differential equation is linear if all terms involving the dependent variable are linear. If even one is nonlinear, the entire equation is classified as nonlinear.

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