How do I solve for a implicit derivative?

I need to solve for the implicit derivatives. How do have Matlab mark or view diff(u(x,y),y) as a variable that it needs to solver for?

Thanks

clear all
clc
syms x y u v;
u = sym('u(x,y)');
v = sym('v(x,y)');
g = x^2 - y^2 + u*v - v^2 +3;
h = x + y^2 + u^2 + u*v - 2;
x = 2;
y = 1;

a = diff(g)
b = diff(h)
c = diff(g,y)
d = diff(h,y)

u = -1
v = 2
[m n o p]=solve(a==0,b==0,c==0,d==0,diff(u(x,y),x),diff(u(x,y),y),diff(v(x,y),x), diff(v(x, y), y))

[Walter Roberson]

Caution #1: when you set "x = 2" after "syms x", then any expression in the symbol "x" will not have "2" substituted for "x". If you want that to happen, use subs()

Caution #2: it is much more robust to explicitly specify which variable you wish to differentiate with respect to.

[Walter Roberson]

They are correctly taking the derivative with respect to x.

Above the point at which the derivative is taken, there is the statement

y = 1;

That overwrites the meaning of y as symbolic in the MATLAB workspace, so when

c = diff(g,y)

is called, the call is

c = diff(g,1)

which asks for the derivative to be taken 1 time with respect to the default variable. The default variable, as determined by symvar() gives first priority to x, as noted in http://www.mathworks.com/help/symbolic/symvar.html#bs_eb_i-3 and the "Algorithms" section a few lines further down.

This is why you should avoid assigning to any variable that you previously defined as symbolic and used in an expression: there is too much chance of confusion over what value the name should have after that point. Use different names for different purposes, and use subs() if you are intentionally replacing names with values.

Answer 1

[Walter Roberson]

You cannot tell the symbolic toolbox to solve for a differential expression. You need to solve for the function and then differentiate the expression. You might have to use dsolve() to solve for the function.

[Mara Gati]

Thanks for this!