Some double angle identity to solve $(2{x}^{2}+{y}^{2})\frac{dy}{dx}=2xy?$

veksetz
2022-01-20
Answered

Some double angle identity to solve $(2{x}^{2}+{y}^{2})\frac{dy}{dx}=2xy?$

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asked 2020-12-12

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform

$L\{3{e}^{-4t}-{t}^{2}+6t-9\}$

asked 2021-03-07

Use the appropriate algebra and Table of Laplaces

asked 2022-09-12

Need to evaluate the Laplace integral transform (definition below) of $\sqrt{t}$ using complex analysis. How is that possible?

$$\hat{f}(s)={\int}_{0}^{\mathrm{\infty}}\sqrt{t}{e}^{-st}dt$$

$$\hat{f}(s)={\int}_{0}^{\mathrm{\infty}}\sqrt{t}{e}^{-st}dt$$

asked 2021-02-04

Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.

a)$F(s)=\frac{3{e}^{-2s}}{s(s+3)}$

b)$F(s)=\frac{{e}^{-2s}}{s(s+1)}$

c)$F(s)=\frac{{e}^{-2s}-{e}^{-3s}}{2}$

a)

b)

c)

asked 2022-09-22

Let $\mathcal{L}[f(x)](s)$ be the Laplace Transformation of a function f(x).

I know ${\mathcal{L}}^{-1}[\frac{1}{s+10}]=\frac{1}{s-(-10)}={e}^{-10x}$

How would I calculate ${\mathcal{L}}^{-1}$ for the expression $\frac{1}{s+10}\mathcal{L}[f(x)]?$? , where f(x) is arbitary.

I know ${\mathcal{L}}^{-1}[\frac{1}{s+10}]=\frac{1}{s-(-10)}={e}^{-10x}$

How would I calculate ${\mathcal{L}}^{-1}$ for the expression $\frac{1}{s+10}\mathcal{L}[f(x)]?$? , where f(x) is arbitary.

asked 2021-11-17

Determine the values of r or which the given differential equation has solutions of the form $y={e}^{rt},\text{}y{}^{\u2033}-3y{}^{\u2033}+2{y}^{\prime}=0$

asked 2021-05-12

One property of Laplace transform can be expressed in terms of the inverse Laplace transform as ${L}^{-1}\left\{\frac{{d}^{n}F}{d{s}^{n}}\right\}(t)=(-t{)}^{n}f(t)$ where $f={L}^{-1}\left\{F\right\}$ . Use this equation to compute ${L}^{-1}\left\{F\right\}$

$F(s)=\mathrm{arctan}\frac{23}{s}$