How I can use mathematica to get the answer of this question
(Using the Runge-Kutta method of order 2 solve
x'(t) = -x (t) + t^0.1 (1.1+t)
x (0)=0
whose solution is ,
x(t)=t^1.1
solve the question on [0,5] printing the solution and the errors at x= 1,3,5
use step- sizes h=0.1 ,0.05,0.025 ,0.0125,0.00625 calculate the ratios by which the error decrease when h is halved
Please show code for what you have already tried!
(Or is the question a homework problem you’re asking us to do for you?)
Have you already tried something simpler, such as applying Euler’s Method?
And why do you want to use Runge-Kutta here to get a numerical solution since you already know an exact solution—which you could find in Mathematica from:
DSolve[{x'[t] == -x[t] + t^(1/10) (11/10 + t), x[0] == 0}, x[t], t]