# Fold Dynamic Function [duplicate]

I'm making on a demo working with differential equations as functions of two variables (x and y). The demo will have to Fold the differential equation with an initial y-value and a series of x-values. Here's a simple code for the demo. The output should be a list on new y-values.

DynamicModule[{dydx = Null},
Deploy@
Panel@
Grid@
Transpose@
{{"Differential equation: (dy/dx)=",
"List of Slopes:"},
{InputField[Dynamic[dydx]],
InputField[Dynamic[FoldList[dydx, 1, {0, 1, 2, 3}]]]}}]


The code doesn't work because dydx cannot be applied as a function in FoldList. "dydx" needs to be defined as a function f[y_,x_]. However, I'm not sure how to dynamically change a function using InputField.

f[y_,x_]= dydx
FoldList[f,1,{0,1,2,3}]


I'd like to have this as part of the Dynamic Module. Users would be able to input a function then receive a list of new y values.