In mathematics, in the field of Differential equations, a boundary value problem is a Differential equations together with a set of additional constraints, called the boundary conditions.

asked 2021-05-03

When talking about boundary conditions for partial Differential equations, what does an open boundary mean?

asked 2021-05-01

Transform the given differential equation or system into an equivalent system of first-order differential equations.

\(\displaystyle{x}^{{{\left({3}\right)}}}={\left({x}'\right)}^{{{2}}}+{\cos{{x}}}\)

\(\displaystyle{x}^{{{\left({3}\right)}}}={\left({x}'\right)}^{{{2}}}+{\cos{{x}}}\)

asked 2021-10-05

Consider the system of differential equations \(\displaystyle{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}=-{y}\ \ \ {\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}=-{x}\).a)Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation.

b)Solve the equation you obtained for y as a function of t; hence find x as a function of t.

b)Solve the equation you obtained for y as a function of t; hence find x as a function of t.

asked 2021-09-07

Explain what is the difference between implicit and explicit solutions for differential equation initial value problems.

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 2021-09-15

Find if the following first order differential equations seperable, linear, exact, almost exact, homogeneous, or Bernoulli. Rewrite the equation into standard form for the classification it fits.

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

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

asked 2021-09-13

Find if the following first order differential equations seperable, linear, exact, almost exact, homogeneous, or Bernoulli. Rewrite the equation into standard form for the classification it fits.

\(\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}={x}^{{2}}{\left[{\left({x}^{{3}}\right)}{\left({y}\right)}-{\left(\frac{{1}}{{x}}\right)}\right]}\)

\(\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}={x}^{{2}}{\left[{\left({x}^{{3}}\right)}{\left({y}\right)}-{\left(\frac{{1}}{{x}}\right)}\right]}\)