Whole derivation of two variable differential function

I am struggleing with the whole derivation of differential equation.

Can y'all give me an advice how to implement that into a code?

I've tried using diff() but diff(f(x,y), y) gives 1 not y'.

Answer 1

[James Tursa]

Please show the code you are using.

y' means derivative of y with respect to x, not derivative of y with respect to y. You should be taking derivative of f(x,y) with respect to x, not y.

[Minjae Cho]

syms x y

f(x, y) = -x^3 + x + 1 +y;

the derivation should be f '(x, y) => y ' - 3*x^2 + 1

but when I do diff(f, x) => - 3*x^2 + 1 [which is partial derivative w.r.t. x].

Is there any way to get a whole derivative rather than a partial derivative?

[Walter Roberson]

Is there any way to get a whole derivative rather than a partial derivative?

syms x y
f = y - x^3 + x + 1

f = 

dy = f

dy = 

df = diff(f, x) + diff(f, y)

df = 

simplify(subs(df, diff(y,x), dy))

ans = 

You may notice that this is not what you wanted... but it satisfies at least one plausible definition of what a "whole derivative" means.

I recommend that you re-examine that derivative provided. I think you will find that it makes no sense unless it is the derivative with respect to x with the assumption that y is a function of x

Answer 2

[Walter Roberson]

The equations are being careless about which variables depend on which variables, and on which variable the differentiation is with respect to.

syms x y(x)
f = y - x^3 + x + 1

f(x) = 

dy = f

dy(x) = 

df = diff(f, x)

df(x) = 

simplify(subs(df, diff(y,x), dy))

ans(x) = 

[Minjae Cho]

then how can I plug the value to y(x)?

ex) later on I have to plug value y=3 to y(x)

[Walter Roberson]

Plug what values into y(x) ?

syms x y(x) yx
f = y - x^3 + x + 1

f(x) = 

dy = f

dy(x) = 

df = diff(f, x)

df(x) = 

sol = simplify(subs(subs(df(x), diff(y,x), dy), y, yx))

sol = 

[X, Y] = ndgrid(linspace(-1, 1, 15));
solgrid = double(subs(sol, {x, yx}, {X, Y}));
whos

  Name          Size            Bytes  Class     Attributes

  X            15x15             1800  double              
  Y            15x15             1800  double              
  cmdout        1x33               66  char                
  df            1x1                 8  symfun              
  dy            1x1                 8  symfun              
  f             1x1                 8  symfun              
  sol           1x1                 8  sym                 
  solgrid      15x15             1800  double              
  x             1x1                 8  sym                 
  y             1x1                 8  symfun              
  yx            1x1                 8  sym                 

surf(X, Y, solgrid)