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Question
Express the following physical statements in the form of differential equation.
A saving amount pays 8% interest per year compound continuously. In addition, the income from another investment is credited to the amount continuously at the rate of ₹ 400 per year.
Solution
Let x be the amount.
Amount varies from every year
(ie) Amount varies with respect to time t is `("d"x)/"dt"` and in addition the income from other source credited ₹ 400 continuously for every year.
∴ `("d"x)/"dt" = 8/100 xx x + 400`
⇒ `("d"x)/"dt" = (2x)/25 + 400`
⇒ `("d"x)/"dt" - 2/25x - 400` = 0 is a required differential equation.
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