Solution Found!
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(choose chapter or problem)
QUESTION:
Do 10 steps. Solve exactly. Compute the error. Show details.
\(y^{\prime}+0.2 y=0, \quad y(0)=5, \quad h=0.2\)
Questions & Answers
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:
\(y' + 0.2y = 0\)
\(y' = - 0.2y\)
\(\frac{{dy}}{{dx}} = - 0.2y\)
\(\frac{{dy}}{y} = - 0.2xdx\)