The solution of the given Differential equations is
\(\displaystyle{y}={2}{\tan{{\left({2}{x}+{c}\right)}}}-{4}{x}\), where c is a constant.

asked 2021-08-21

\(\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}\)

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 2021-11-17

Find y" by implicit differentiation.

\(\displaystyle{x}^{{2}}+{4}{y}^{{2}}={4}\)

\(\displaystyle{x}^{{2}}+{4}{y}^{{2}}={4}\)

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 2021-10-21

Find the solution of the given initial value problem. \(\displaystyle{y}'−{2}{y}={e}{2}{t},{y}{\left({0}\right)}={2}\)

asked 2021-10-17

A part icle moves along the curve \(\displaystyle{y}={2}{\sin{{\left(\pi\frac{{x}}{{2}}\right)}}}\). As the particle passes through the point \(\displaystyle{\left(\frac{{1}}{{3}},{1}\right)}\) its x-coordinate increases at a rate of \(\displaystyle\sqrt{{{10}}}\) cm/s. How fast is the distance from the particle to the origin changing at this instant?

asked 2021-10-19

Find \(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{x}\right.}}}}\) and \(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{y}\right.}}}}\).

\(\displaystyle{z}={\frac{{{x}{y}}}{{{x}^{{2}}+{y}^{{2}}}}}\)

\(\displaystyle{z}={\frac{{{x}{y}}}{{{x}^{{2}}+{y}^{{2}}}}}\)