Whole derivation of two variable differential function

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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'.

Answers (2)

James Tursa
James Tursa on 22 Jun 2022
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.
  2 Comments
Walter Roberson
Walter Roberson on 22 Jun 2022
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

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Walter Roberson
Walter Roberson on 22 Jun 2022
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) = 
  2 Comments
Walter Roberson
Walter Roberson on 22 Jun 2022
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)

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