13: Intro to Differential Equations

The scent of a certain air freshener evaporates at a rate proportional to the amount of the air freshener present. Half of the air freshener evaporates within $2$ hours of being sprayed. If the scent of the air freshener is undetectable once $80\%$ has evaporated, how long will the scent of the air freshener last?

Find the particular solution that satisfies the given initial condition

$\(\left\)(y^2+y\(\right\))e^{x}y^{\(\prime\)}=y^3+e^{x}y^3;y\(\left\)(0\(\right\))=1$

Find the general solution to the differential equation.

$\(\frac{dy}{dx}\)=y\(\sqrt{x}\)$

$\$2,000$ is invested in an account that earns interest at a rate of $8.5\%$ and is compounded continuously. Find the particular solution that describes the growth of this account in dollars $A$ after $t$ years. Hint: When interest is compounded continuously, it grows exponentially with a growth constant equivalent to the interest rate.