Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) use euler's method with time step h=0.2 to approximate y(0.2),y(0.(1.0) . k tk yk 0 0 3 1 0.2 equation editor equation editor 2 0.4 equation editor equation editor 3 0.6 equation editor equation editor 4 0.8 equation editor equation editor 5 1.0 equation editor equation editor (b) use separation of variables to find y(t) exactly. y(t) = equation editor equation editor (c) compute the error in the approximations to y(0.2),y(0.6) , and y(1). |y(0.2)−y1|=

Step-by-step explanation:

Point a:

The Euler's method states that:

where

We have that , , ,

So you need to:

So you need to:

The Euler's Method is detailed in the following table.

Point b:

To find the general solution of you need to:

Rewrite in the form of a first order separable ODE:

Integrate each side:

We know the initial condition y(0) = 3, we are going to use it to find the value of

So we have:

Solving for y we get:

Point c:

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using

Next, where are from the table.

step-by-step explanation:

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