Question

Given the system of first order differential equations below use Runge Kuta 4th Order

dy = -2y + 5e-t dt dx -yx dt 2

varying from a range of t=0 to 0.4 and step size 0.2 Given x(0)=4 and y(0)=2

Find the solution of x at t=0.2

Select one:

a. 2.08256

b. 1.36864

c. 2.18677

d. 1.58347

e. None of the given options

Answer 1

Answer is (c).

First, solved the ODE in y with given initial value y(0)=2. To find y(t).

-2y + 56 & 9 10) = 2. given, dy dt first we'll solve for y. Sadt factora e integrating 2t. -t = 5e dy tay dt 2t multiply by eat. e et dy it tae عه = 5et. - 2t. iter (ye 2t j = 5et integrating both sides gives ye?t=set + '+c. => y =50 t + cé using y(o)=2 72=5+c =7 puting t=0&y=2 C-3 -at so, - Зе y= 5é - t Зе e ty 5e Х 22 Now, dx dt -yx² 2 2 f(t, x) Now, we'lll apply sunge kutta of 4th order to find X (0:2).

Then it's easy to apply Runge Kutta of 4th order to find value of x at 0.2. as below.