Differential Equations: Families of Solutions (Level 4 of 4)

The video tutorial explains how to verify a piecewise defined function as a solution to a differential equation. It covers the verification process across three intervals: negative infinity to zero, at zero, and zero to positive infinity. The tutorial emphasizes the importance of continuity and differentiability in verifying solutions. It concludes by confirming the piecewise function as a valid solution and introduces the next topic on systems of differential equations.

Explain how to verify that a piecewise defined function is a solution to a differential equation.

What is the piecewise defined function that needs to be verified as a solution to the differential equation?

What are the intervals for which the piecewise defined function is defined?

How do you determine if the piecewise defined function is continuous and differentiable at the given intervals?

What is the significance of verifying the piecewise defined function at X equals zero?

Describe the process of finding the limits as X approaches zero from both sides for the derivative.

What conclusion can be drawn about the piecewise defined function after verifying all three sections?