Question: I need the code in detail for ODE solution in JavaScript ( ECMASCRIPT program ) Consider a first order ordinary differential equation given by: y

I need the code "in detail" for ODE solution in JavaScript ( ECMASCRIPT program )
Consider a first order ordinary differential equation given by:
y ' = f (x,y) = y*x^2 -1.2y
with a starting value of y (0) = 1 on the interval x = 0 to 2 with n = 8 (step size will be h = 0.25 )
determine the value of y (2) using:
(a) Euler's method
on each interval the next y value = previous y value + slope times step size.
or yn = y + f(x,y) * h
(b) Heun's method
k1 = f ( x, y )
k2 = f ( x+h, y+k1*h )
and
yn = y + (k1 + k2) * h / 2
(c) RK-3 method
k1 = f ( x, y )
k2 = f ( x+h/2, y+k1*h/2 )
k3 = f ( x+h, y -k1*h + 2*k2*h)
and
yn = y + (k1 + 4*k2 + k3) * h/6
(d) RK-4 method
k1 = f ( x, y )
k2 = f ( x+h/2, y+k1*h/2 )
k3 = f ( x+h/2, y+k2*h/2 )
k4 = f ( x+h, y + k3*h)
and
yn = y + (k1 + 2*k2 + 2*k3 + k4) * h / 6
at the start of the program I need you to define:
function f (x,y)
initial values: x = 0 and y = 1
final value: b = 2
number of steps: n = 8
you will need to display the four ending values for y:
(a) Euler's method
(b) Heun's method
(c) RK-3 method
(d) RK-4 method

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