List of practice Questions

The concentration \(p\) (in \(\mu g/dL\) i.e., micrograms/deciliter) of a hormone, as a function of time \(t\) (in hours) is governed by the following differential equation for \(t \geq 0\)

\[ \frac{dp}{dt} = e^{-0.1t} - 0.1\, p \]

If \(p(0) = 20\ \mu g/dL\), then \(p(10) =\) \(\mu g/dL\). (Round off to one decimal place)

Find the solution of the differential equation: \[ \frac{dy}{dx} = 3x^2 \]

Find the general solution of the separable differential equation: \[ \frac{dy}{dx} = e^{x-y} + x^2e^{-y} \]

Find the general solution of the differential equation: \( \frac{dy}{dx} + \frac{y}{x} = x^2 \)