Which one of the following is correct if we differentiate the equation xy = ae^x + be^-x two times?

(a) x(d^2y/ dx) + 2(dy/dx) = xy

(b) x(d^2y/ dx) – 2(dy/dx) = xy

(c) 3x(d^2y/ dx) + 2(dy/dx) = xy

(d) x(d^2y/ dx) + 2(dy/dx) = 2xy

This question was posed to me in an interview for internship.

I need to ask this question from Linear Second Order Differential Equations in chapter Differential Equations of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

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Correct choice is (a) x(d^2y/ dx) + 2(dy/dx) = xy

To explain: We have xy = ae^x + be^-x ……(1)

Differentiating (1) with respect to x, we get

x(dy/dx) + y = ae^x + be^-x …..(2)

Differentiating (2) now, with respect to x, we get

x(d^2y/ dx) + dy/dx + dy/dx = ae^x + be^-x

From (1),

ae^x + be^-x = xy, so that we get

x(d^2y/ dx) + 2(dy/dx) = xy

which is the required differential equation.