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
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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
ae^x + be^-x = xy, so that we get
x(d^2y/ dx) + 2(dy/dx) = xy
which is the required differential equation.