veksetz
2021-12-31
Answered

Identify the characteristic equation, solve for the characteristic roots, and solve the 2nd order differential equations.

$(18{D}^{3}-33{D}^{2}+20D-4)y=0$

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asked 2021-12-28

Find general solutions (implicit if necessary, explicit if convenient) of the differential equations in Problem. Primes denote derivatives with respect to x.

$\frac{dy}{dx}={\left(64xy\right)}^{\frac{1}{3}}$

asked 2021-01-08

Determine L[f]

Let f be a function defined on an interval

The Laplace transform of f is the function F(s) defined by

provided that the improper integral converges. We will usually denote the Laplace transform of f by L[f].

asked 2022-09-05

I know that the Laplace transform of a function f(t) on $[0,\mathrm{\infty})$ is defined as

$${f}^{\ast}(\theta )={\int}_{0}^{\mathrm{\infty}}{e}^{-\theta t}f(t)\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}t.$$

But if I only have ${f}^{\ast}(\theta )={\displaystyle \frac{3+10\theta}{24{\theta}^{2}+22\theta +3}}$, how to evaluate f(t)?

$${f}^{\ast}(\theta )={\int}_{0}^{\mathrm{\infty}}{e}^{-\theta t}f(t)\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}t.$$

But if I only have ${f}^{\ast}(\theta )={\displaystyle \frac{3+10\theta}{24{\theta}^{2}+22\theta +3}}$, how to evaluate f(t)?

asked 2021-12-30

Solve both the differential equations. $({y}^{2}+1)dx+(2xy+1)dy=0$

asked 2020-11-23

Solve the given symbolic initial value problem and sketch a graph of the solution.

$y\prime \prime +y=3\delta (t-(\frac{\pi}{2})y(0)=0{y}^{\prime}(0)=3$

asked 2021-05-21

A population like that of the United States with an age structure of roughly equal numbers in each of the age groups can be predicted to A) grow rapidly over a 30-year-period and then stabilize B) grow little for a generation and then grow rapidly C) fall slowly and steadily over many decades D) show slow and steady growth for some time into the future

asked 2022-01-19

How to solve $y}^{\prime}+y={e}^{x}{y}^{\frac{2}{3}$ ?