Do 10 steps. Solve exactly. Compute the error. Show details. \(y^{\prime}+0.2 y=0, \quad y(0)=5, \quad h=0.2\)

Chapter 21, Problem 1

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QUESTION:

Do 10 steps. Solve exactly. Compute the error. Show details.

\(y^{\prime}+0.2 y=0, \quad y(0)=5, \quad h=0.2\)

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QUESTION:

Do 10 steps. Solve exactly. Compute the error. Show details.

\(y^{\prime}+0.2 y=0, \quad y(0)=5, \quad h=0.2\)

ANSWER:

Step 1 of 12

The formula regarding Euler’s method is as follows:

\({y_{n + 1}} = {y_n} + hf\left( {{x_n},{y_n}} \right)\,\,\,(n = 0,1,2.......)\)

As per the given information we have

\(y' + 0.2y = 0,y\left( 0 \right) = 5,h = 0.2\)

The differential equation can be solved as follows:

\(y' + 0.2y = 0\)

\(y' =  - 0.2y\)

\(\frac{{dy}}{{dx}} =  - 0.2y\)

\(\frac{{dy}}{y} =  - 0.2xdx\)

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