Applications of Differential Equations

Find the differential equation form of $V=iR$ with respect to change in time. If $V=26$ volts, $i=2$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=12$ volts, $i=4$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=24$ volts, $i=4$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=24$ volts, $i=2$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=20$ volts, $i=2$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=26$ volts, $i=2$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=12$ volts, $i=4$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=24$ volts, $i=4$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=24$ volts, $i=2$ Amperes, then find $R$ in ohms.

Find the differential equation form of $V=iR$ with respect to change in time. If $V=20$ volts, $i=2$ Amperes, then find $R$ in ohms.

A tank contains $40 \mathrm{l}$ of solution containing $2 \mathrm{g}$ of substance per liter. Salt water containing $3 \mathrm{g}$ of this substance per liter runs in at the rate of $4 \frac{l}{\min }$ and the well - stirred mixture runs out at the same rate. Find the amount of substance in the tank after $50$ minutes. [Use, $\frac{1}{e^5}=0.006737947$]

A tank contains $40 \mathrm{l}$ of solution containing $2 \mathrm{g}$ of substance per liter. Salt water containing $3 \mathrm{g}$ of this substance per liter runs in at the rate of $4 \frac{l}{\min }$ and the well - stirred mixture runs out at the same rate. Find the amount of substance in the tank after $30$ minutes. [Use, $\frac{1}{e^3}=0.0497870684$]

A tank contains $40 \mathrm{l}$ of solution containing $2 \mathrm{g}$ of substance per liter. Salt water containing $3 \mathrm{g}$ of this substance per liter runs in at the rate of $4 \frac{l}{\min }$ and the well - stirred mixture runs out at the same rate. Find the amount of substance in the tank after $20$ minutes. [Use, $\frac{1}{e^2}=0.135335283$]

A tank contains $40 \mathrm{l}$ of solution containing $2 \mathrm{g}$ of substance per liter. Salt water containing $3 \mathrm{g}$ of this substance per liter runs in at the rate of $4 \frac{l}{\min }$ and the well - stirred mixture runs out at the same rate. Find the amount of substance in the tank after $10$ minutes. [Use, $\frac{1}{e}=0.367879441$]

A tank contains $40 \mathrm{l}$ of solution containing $2 \mathrm{g}$ of substance per liter. Salt water containing $3 \mathrm{g}$ of this substance per liter runs in at the rate of $4 \frac{l}{\min }$ and the well - stirred mixture runs out at the same rate. Find the amount of substance in the tank after $15$ minutes. [Use, $e^{-1.5}=0.22313016$]

The population grows at the rate of $8\%$ per year. Find the time taken for the population to become double in years. Given: $\log 2=0.6912$

In a culture of yeast the active ferment doubles itself in $3$ hours. Assuming that the quantity increases at a rate proportional to itself, determine the number of times it multiplies itself in $15$ hours.

Find the half life of uranium, which disintegrates at a rate proportional to the amount present at any instant. Given that $m_1$ and $m_2$ grams of uranium are present at time $t_1$ and $t_2$ respectively

The bacteria culture grows at a rate proportional to its size. After $2$ hours, there are $600$ bacteria and after $8$ hours the count is $75,000$. Find the initial population and when will the population reach $2,00,000$ ?

The rate of growth of the population is proportional to the number present. If the population doubled in the last $25$ years and the present population is $1$ lac, when will the city have population $4,00,000$$?$