Question

asked 2021-05-29

Solve the given differential equation by separation of variables:

\(\frac{dP}{dt}=P-P^2\)

\(\frac{dP}{dt}=P-P^2\)

asked 2021-03-22

Solve the equation:

\(\displaystyle{\left({x}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}{\left({y}^{{2}}+{1}\right)}\)

\(\displaystyle{\left({x}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}{\left({y}^{{2}}+{1}\right)}\)

asked 2021-05-11

Solve the differential equation by variation of parameters

\(y" + 3y' +2y = \frac{1}{1+e^x}\)

\(y" + 3y' +2y = \frac{1}{1+e^x}\)

asked 2021-05-03

Find \(\frac{dy}{dx}\) and \(\frac{d^2y}{dx^2}.x=e^t,y=te^{-t}\). For which values of t is the curve concave upward?