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प्रश्न
The solution of the differential equation `dx/dt = (xlogx)/t` is ______.
विकल्प
x = ect
x + ect = 0
x = et + t
xect = 0
उत्तर
The solution of the differential equation `dx/dt = (xlogx)/t` is x = ect.
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
∴ ect = x
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