The answer is given below in the photo

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?

asked 2021-09-09

\(\displaystyle{x}={e}^{{{t}}},{y}={t}{e}^{{−{t}}}\)

For which values of t is the curve concave upward?

asked 2021-11-15

Solve the diﬀerential equation

\(\displaystyle{\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}}-{2}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{4}{y}={e}^{{x}}{{\sin}^{{2}}{\left({\frac{{{x}}}{{{2}}}}\right)}}\)

\(\displaystyle{\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}}-{2}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{4}{y}={e}^{{x}}{{\sin}^{{2}}{\left({\frac{{{x}}}{{{2}}}}\right)}}\)

asked 2021-11-05

Find the general solution for the following differential equation.

\(\displaystyle{\frac{{{d}^{{{3}}}{y}}}{{{\left.{d}{x}\right.}^{{{3}}}}}}-{\frac{{{d}^{{{2}}}{y}}}{{{\left.{d}{x}\right.}^{{{2}}}}}}-{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{y}={x}+{e}^{{-{x}}}\).

\(\displaystyle{\frac{{{d}^{{{3}}}{y}}}{{{\left.{d}{x}\right.}^{{{3}}}}}}-{\frac{{{d}^{{{2}}}{y}}}{{{\left.{d}{x}\right.}^{{{2}}}}}}-{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{y}={x}+{e}^{{-{x}}}\).

asked 2021-05-17

Compute \(\triangle y\) and dy for the given values of x and \(dx=\triangle x\)

\(y=x^2-4x, x=3 , \triangle x =0,5\)

\(\triangle y=???\)

dy=?

\(y=x^2-4x, x=3 , \triangle x =0,5\)

\(\triangle y=???\)

dy=?

asked 2021-09-20

Compute \(\displaystyle\triangle{y}\) and dy for the given values of x and \(\displaystyle{\left.{d}{x}\right.}=\triangle{x}\)

\(\displaystyle{y}={x}^{{2}}-{4}{x},{x}={3},\triangle{x}={0},{5}\)

\(\displaystyle\triangle{y}=???\)

dy=?

\(\displaystyle{y}={x}^{{2}}-{4}{x},{x}={3},\triangle{x}={0},{5}\)

\(\displaystyle\triangle{y}=???\)

dy=?

asked 2021-11-21

\(x = t^2+ 1,\ y = t^2 + t\)