Stefan Hendricks

2021-12-31

Let $y\left(t\right)$ be the solution to $y=7t{e}^{-y}$ satisfying $y\left(0\right)=2$ .

(a) Use Euler's Method with time step$h=0.2$ to approximate $y\left(0.2\right),y\left(0.4\right),\dots ,y\left(1.0\right)$ .

(b) Use separation of variables to find y(t) exactly.

(c) Compute the error in the approximations to$y\left(0.2\right),y\left(0.6\right)$ , and $y\left(1\right)$ .

(a) Use Euler's Method with time step

(b) Use separation of variables to find y(t) exactly.

(c) Compute the error in the approximations to

autormtak0w

Beginner2022-01-01Added 31 answers

Step 1

Let$y=f(t,y),y\left({t}_{0}\right)={y}_{0}$ be given IvP

The by Eulers

Let

The by Eulers

Ethan Sanders

Beginner2022-01-02Added 35 answers

Step 3

$y=\frac{dy}{dt}7t{e}^{-y}$ - (1) $y\left(0\right)=2$ -(2)

$\Rightarrow \frac{dy}{{e}^{-y}}=7tdt$

$\Rightarrow \int {e}^{y}dy=\int 7tdt+c$

$\Rightarrow {e}^{y}=\frac{7{t}^{2}}{2}+c$

Using (2) we get,

${e}^{2}=c$

$\therefore {e}^{y}=\frac{7{t}^{2}}{2}+{e}^{2}$

$\Rightarrow y\left(t\right)={\mathrm{log}}_{e}[\frac{7{t}^{2}}{2}+{e}^{2}]$

Using (2) we get,

karton

Expert2022-01-09Added 613 answers

Step 4

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