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.

What is the differential equation that the piecewise function is being verified against?

• Y Prime plus 4Y equals zero

• X times Y Prime - 4Y equals zero

• X times Y Prime plus 4Y equals zero

• Y Prime minus 4Y equals zero

In the interval from negative infinity to zero, what is the form of the piecewise function?

• X raised to the power of 4

• Negative X raised to the power of 4

• X squared

• Negative X squared

What must be verified about the piecewise function at X equals zero?

• It is neither continuous nor differentiable

• It is only continuous

• It is only differentiable

• It is continuous and differentiable

What is the derivative of the piecewise function as X approaches zero from the left?

• -X cubed

• 4X cubed

• -4X cubed

• X cubed

What is the derivative of the piecewise function as X approaches zero from the right?

• -X cubed

• X cubed

• -4X cubed

• 4X cubed

In the interval from zero to positive infinity, what is the form of the piecewise function?

• X squared

• Negative X raised to the power of 4

• X raised to the power of 4

• Negative X squared

What is the result of verifying the piecewise function in all intervals?

• The function is not a solution to the differential equation

• The function is a solution only in one interval

• The function is a solution only at X equals zero

• The function is a solution in all intervals