Question

The solution of the differential equation `dx/dt = (xlogx)/t` is ______.

Options

• x = e^ct

• x + e^ct = 0

• x = e^t + t

• xe^ct = 0

Answer 1

The solution of the differential equation `dx/dt = (xlogx)/t` is x = e^ct.

Explanation:

`dx/dt = (xlogx)/t`

∴ `dx/(xlogx) dt/t`

Integrating both sides, we get

`int dx/(xlogx) = int dt/t`

∴ log (log x) = log (t) + log c

∴ log (log x) = log (tc)

∴ log x = ct

∴ e^ct = x