Euler’s method
Consider the initial-value problem y′ = −2y, y(0) = 1. The
analytic solution is y(x) = e−2x . (a) Approximate y(0.1) using one
step of Euler’s method. (b) Find a bound for the local truncation
error in y1 . (c) Compare the error in y1 with your error bound.
(d) Approximate y(0.1) using two steps of Euler’s method. (e)
Verify that the global truncation error for Euler’s method is O(h)
by comparing the errors in parts (a) and...
Solve the initial value problem
y′=(2cos(2x))/(3+2y), y(0)=−1
and determine where the solution attains its maximum value (for
0≤x≤1.697).
Enclose arguments of functions in parentheses. For example,
sin(2x).
Y(x)=?
x=?
10. Solve the following initial value problem:
y''' − 2y '' + y ' = 2e ^x − 4e^ −x
y(0) = 3, y' (0) = 1, y''(0) = 6
BOTH LINES ARE PART OF A SYSTEM OF EQUATIONS