Donald Johnson
2021-12-29
Answered

A steel ball of mass 4-kg is dropped from rest from the top of a building. If the air resistance is 0.012v and the ball hits the ground after 2.1 seconds, how tall is the building? Answer in four decimal places.

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asked 2021-11-14

Find the general solution of the given differential equation.

${y}^{\left(6\right)}+y=0$

asked 2022-09-07

Try to solve the follow equation:

$${y}^{\mathrm{\prime}\mathrm{\prime}}+y=\{\begin{array}{ll}{t}^{2}& 0\le t\le 1,\\ 0& \text{else}\end{array}$$

with the initial conditions $y(0)={y}^{\mathrm{\prime}}(0)=0$. I get an expresion for the laplace transfor of y:

$$L(y)=\frac{1-{e}^{-s}}{s({s}^{2}+1)}+\frac{1-{e}^{-s}}{{s}^{2}({s}^{2}+1)}+\frac{1-{e}^{-s}}{{s}^{3}({s}^{2}+1)}.$$

$${y}^{\mathrm{\prime}\mathrm{\prime}}+y=\{\begin{array}{ll}{t}^{2}& 0\le t\le 1,\\ 0& \text{else}\end{array}$$

with the initial conditions $y(0)={y}^{\mathrm{\prime}}(0)=0$. I get an expresion for the laplace transfor of y:

$$L(y)=\frac{1-{e}^{-s}}{s({s}^{2}+1)}+\frac{1-{e}^{-s}}{{s}^{2}({s}^{2}+1)}+\frac{1-{e}^{-s}}{{s}^{3}({s}^{2}+1)}.$$

asked 2021-12-29

Solve the given differential equation. If an initial condition is given, also find the solution that satisfies it.

$({e}^{x}+1)\frac{dy}{dx}=y-y{e}^{x}$

asked 2022-01-19

Solve: $\frac{dp}{dt}={t}^{2}p-p+{t}^{2}-1$

I got$\int \frac{1}{p+1}dp=\int ({t}^{2}-1)dt$

After take the integral I got

$\mathrm{ln}|p+1|+c=\frac{1}{3}{t}^{2}-t+c$

after this step I stacked. How can I simplify like$p=$ something?

I got

After take the integral I got

after this step I stacked. How can I simplify like

asked 2021-01-15

Let $y(t)={\int}_{0}^{t}f(t)dt$ If the Laplace transform of y(t) is given $Y(s)=\frac{19}{({s}^{2}+25)}$ , find f(t)

a)$f(t)=19\mathrm{sin}(5t)$

b) none

c)$f(t)=6\mathrm{sin}(2t)$

d)$f(t)=20\mathrm{cos}(6t)$

e)$f(t)=19\mathrm{cos}(5t)$

a)

b) none

c)

d)

e)

asked 2021-02-08

Use the Laplace transform to solve the following initial value problem:

$2y"+4{y}^{\prime}+17y=3\mathrm{cos}(2t)$

$y(0)={y}^{\prime}(0)=0$

a)take Laplace transform of both sides of the given differntial equation to create corresponding algebraic equation and then solve for$L\{y(t)\}$ b) Express the solution $y(t)$ in terms of a convolution integral

a)take Laplace transform of both sides of the given differntial equation to create corresponding algebraic equation and then solve for

asked 2021-09-14

If the

a)

b)

c)

d) None of these