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An ordinary differential equation is given below. (dy/dx)(x ln x) = y The solution for the above equation is (Note: K denotes a constant in the options)

1. y = Kx ln x
2. y = Kxe^x
3. y = Kxe^(-x)
4. y = K ln x

Correct answer: y = K ln x

Solution

From (x ln x) dy/dx = y, separate to dy/y = dx/(x ln x). The right side integrates to ln|ln x|, so ln y = ln(ln x) + C, giving y = K ln x. The stored answer y = Kx ln x is wrong.

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