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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 |
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Answer» Correct Answer - Option 2 : y'' - 8y' + 16y = 0 Concept: To form the differential equation of the given equation
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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