The solution of $\frac{d^2 y}{d x^2}=0$ represents

The population $p$ of the city at time $t$ is given by $\frac{dp}{dt} = \frac{p}{2} - 100$. If the initial population at $t = 0$ is $100$,then $p$ is:

In a bank,the principal increases continuously at the rate of $r \%$ per year. Find the value of $r$ if $Rs \, 100$ doubles itself in $10$ years $\left(\log _{e} 2=0.6931\right)$. (in $\%$)

In a culture,the bacteria count is $1,00,000$. The number increases by $10 \%$ in $2$ hours. In how many hours will the count reach $2,00,000$,if the rate of growth of bacteria is proportional to the number present?

The solution of the differential equation $x \frac{d^2y}{dx^2} = 1$,given that $y = 1$ and $\frac{dy}{dx} = 0$ when $x = 1$,is

The population $P=P(t)$ at time $t$ of a certain species follows the differential equation $\frac{dP}{dt}=0.5 P-450$. If $P(0)=850$,then the time at which the population becomes zero is