uppose that we use Euler's method to approximate the solution to the differential equation dy dx y(0.3) = 4. %3D et f(x, y) = æ²/y. Ve let ro = 0.3 and yo = 4 and pick a step sizeh = 0.2. Euler's method is the the following algorithm. From x, and yn, our approximations to the solution of the differential equation at the nth stage, we nd the next stage by computing In+1 = r, + h, Yn+1 = Yn + h · f(xm, Yn). somplete the following table. Your answers should be accurate to at least seven decimal places. Yn 0.3 4 he exact solution can also be found using separation of variables. It is (2) = hus the actual value of the function at the point a = 1.3 (1.3) =
uppose that we use Euler's method to approximate the solution to the differential equation dy dx y(0.3) = 4. %3D et f(x, y) = æ²/y. Ve let ro = 0.3 and yo = 4 and pick a step sizeh = 0.2. Euler's method is the the following algorithm. From x, and yn, our approximations to the solution of the differential equation at the nth stage, we nd the next stage by computing In+1 = r, + h, Yn+1 = Yn + h · f(xm, Yn). somplete the following table. Your answers should be accurate to at least seven decimal places. Yn 0.3 4 he exact solution can also be found using separation of variables. It is (2) = hus the actual value of the function at the point a = 1.3 (1.3) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that we use Euler's method to approximate the solution to the differential equation
dy
y(0.3) = 4.
da
Let f(x, y) = x? /y.
We let xo = 0.3 and yo = 4 and pick a step size h = 0.2. Euler's method is the the following algorithm. From xn and yn, our approximations to the solution of the differential equation at the nth stage, we
find the next stage by computing
In+1 = x, +h,
Yn+1 = Yn + h · f(xn, Y,).
Complete the following table. Your answers should be accurate to at least seven decimal places.
n
In
Yn
0.3
The exact solution can also be found using separation of variables. It is
y(x) =
Thus the actual value of the function at the point x = 1.3
y(1.3) =
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