Differential equations problems, solved and explained - PlainMath

Recent questions in Differential equations

Russell Gillen 2021-12-31 Answered

Find the general solution of the given second-order differential equation.
3y''+2y'+y=0

Donald Johnson 2021-12-15 Answered

How do you find \(\displaystyle{\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}}\) by implicit differentiation where \(\displaystyle{x}^{{2}}{y}+{x}{y}^{{2}}={3}{x}\)

fertilizeki 2021-12-13 Answered

Find the differential.
a) \(\displaystyle{z}={\frac{{{1}}}{{{2}}}}{\left({e}^{{{x}^{{{2}}}+{y}^{{{2}}}}}-{e}^{{-{x}^{{{2}}}-{y}^{{{2}}}}}\right)}\)
b) \(\displaystyle{w}={2}{z}^{{{3}}}{y}{\sin{{x}}}\)

Mary Reyes 2021-12-12 Answered

Find the general solution of the given higher-order differential equation.
\(\displaystyle{y}^{{{\left({4}\right)}}}+{y}{'''}+{y}{''}={0}\)
\(\displaystyle{y}{\left({x}\right)}=\)

fortdefruitI 2021-10-23 Answered

Find the general solution of the given differential equation. Give the largest interval over which the general solution is defined. Determine whether there are any transient terms in the general solution.
\(\displaystyle{\cos{{x}}}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{\left({\sin{{x}}}\right)}{y}={1}\)

Efan Halliday 2021-10-21 Answered

Solve the given differential equation by separation of variables.
\(\displaystyle{\csc{{y}}}{d}{x}+{{\sec}^{{{2}}}{x}}{d}{y}={0}\)

bobbie71G 2021-10-19 Answered

verify that each given function is a solution of the differential equation \(\displaystyle{t}{y}'−{y}={t}{2};{y}={3}{t}+{t}^{{2}}\)

Chardonnay Felix 2021-10-18 Answered

\(\displaystyle{\left({x}-{y}\right)}{\left.{d}{x}\right.}+{x}{\left.{d}{y}\right.}={0}\)
Please, solve by using an appropriate substitution.

ankarskogC 2021-10-09 Answered

Solve the equation explicitly for y and differentiate to get y’ in terms of x. \(\displaystyle{\frac{{{1}}}{{{x}}}}+{\frac{{{1}}}{{{y}}}}={1}\)

Anonym 2021-10-08 Answered

Use a linear approximation (or differentials) to estimate the given number. (1.999)4

Rui Baldwin 2021-09-15 Answered

Find transient terms in this general solution to a differential equation, if there are any
\(\displaystyle{y}={\left({x}+{C}\right)}{\left({\frac{{{x}+{2}}}{{{x}-{2}}}}\right)}\)

Elleanor Mckenzie 2021-09-13 Answered

\(\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}=-\frac{{{y}^{{2}}+{x}^{{2}}}}{{{2}{x}{y}}}{\quad\text{and}\quad}{y}{\left({1}\right)}={4}\)
Please, solve the differential equation. Write the method you used and solve for the dependent variable it it is possible.

Kaycee Roche 2021-09-13 Answered

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

preprekomW 2021-09-10 Answered

If \(\displaystyle{x}^{{2}}+{x}{y}+{y}^{{3}}={1}\) find the value of y''' at the point where x = 1

Trent Carpenter 2021-09-09 Answered

First using a trigonometric
identity, find \(\displaystyle{L}{\left\lbrace{f{{\left({t}\right)}}}\right\rbrace}\)
\(\displaystyle{f{{\left({t}\right)}}}={\sin{{2}}}{t}{\cos{{2}}}{t}\)

Rivka Thorpe 2021-09-09 Answered

Find the length of the curve. \(\displaystyle{r}{\left({t}\right)}={<}{8}{t},{t}^{{2}},{\frac{{{1}}}{{{12}}}}{t}^{{3}}{>},{0}\leq{t}\leq{1}\)

Suman Cole 2021-09-09 Answered

If \(\displaystyle{x}{y}+{6}{e}^{{y}}={6}{e}\) , find the value of y" at the point where x=0

CoormaBak9 2021-09-09 Answered

Solve the differential equation by variation of parameters
\(\displaystyle{y}\text{}+{3}{y}'+{2}{y}={\frac{{{1}}}{{{1}+{e}^{{x}}}}}\)

Ramsey 2021-09-09 Answered

Solve the given differential equation by separation of variables: \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}\sqrt{{{1}-{y}^{{2}}}}\)

Cheyanne Leigh 2021-09-07 Answered

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

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