Homework SourseFirst solve the initial value problem x2x5y y4x2y x02 y03 ex
First, solve the initial value problem
x\'=2x-5y
y\'=4x-2y
x(0)=2, y(0)=3
explicitly. Then, using Euler\'s method, find an approximation to the solution of this initial value problem on the interval [0;0.6] with the step h=0.2. Compare the results.
PLEASE SHOW YOUR PROCESS ^^
x\'=2x-5y
y\'=4x-2y
x(0)=2, y(0)=3
explicitly. Then, using Euler\'s method, find an approximation to the solution of this initial value problem on the interval [0;0.6] with the step h=0.2. Compare the results.
PLEASE SHOW YOUR PROCESS ^^
Solution
sX(s) - 2 = 2X(s) - 5Y(s)
sY(s) - 3 = 4X(s) - 2Y(s)
(s-2)X(s) + 5Y(s) = 2
-4X(s) + (s+2)Y(s) = 3
X(s) = (2s-11)/(s^2 + 16)
Y(s) = (3s+2)/(s^2 + 16)
x(t) = 2cos(4t) - (11/4)sin(4t)
y(t) = 3cos(4t) + 0.5sin(4t)
Euler\'s method
x0 = 2, y0 = 3
x1 = 2 + 0.2(4 - 15) = -0.2
y1 = 3 + 0.2(8 - 6) = 3.4
x2 = -0.2 + 0.2(-17.4) = -3.68
y2 = 3.4 + 0.2(-7.6) = 1.88
x3 = -3.68 + 0.2(-16.76) = -7.032
y3 = 1.88 + 0.2(-18.48) = -1.816
