Consider the ordinary differential equation :- dy/dx=2xy with y=1 and x=1?

Question

Consider the ordinary differential equation :- dy/dx=2xy with y=1 and x=1?
try to obtain estimates of the value of y when x = 1.6 by using The fourth-order Runge-Kutta method :

Yn+1 = Yn + 1/6(k1+ 2K2+2k3=k4)

Where

k1= hf(Xn,Yn)
k2= hf(Xn+1/2h ,Yn+ 1/2K1)
k3= hf(Xn+1/2h ,Yn+ 1/2K2)
k4= hf(Xn+h ,Yn+K3)

Answer 1

I guess this is a textbook question, but the application is a poor one since this equation is easily solved analytically by seperating variables,
i.e.,
int. (1/y) dy = 2 int. x dx + c
ln y = x^2 + c
where c is an arbitrary constant.
since x =1 and y=1 , c =-1

Answer 2

Your original assumption is incorrect. If both Y and X equal 1, than the expression is false.

Answer 3

Thanks for educating us