1.

Form the differential equation of the following equation y = e4x(a + bx)1. y'' - 8y' - 16y = 02. y'' - 8y' + 16y = 03. y'' + 4y' + 16y = 04. y'' - 4y' + 16y = 0

Answer» Correct Answer - Option 2 : y'' - 8y' + 16y = 0

Concept:

To form the differential equation of the given equation

  • Differentiate the equation, the number of times as many as the constants are there.
  • Find out the constants in terms of the variables.
  • Substitute the variables in the original equation.


Calculation:

Given equation is y = e4x(a + bx)

There are 2 constants a and b so differentiate 2 times

⇒ y' = 4ae4x + be4x + 4bxe4x

⇒ y' = 4e4x(a + bx) + be4x

⇒ y' = 4y + be4x 

⇒ be4x = y' - 4y

Differentiating one more time 

⇒ 4be4x = y'' - 4y'

⇒ 4(y' - 4y) = y'' - 4y'

⇒ y'' - 8y' + 16y = 0



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