Symbolic function- differential equation sloving

How can I find the maximum or minimum values of the answer of a differential equation after solving it? It returns Symbolic Function as the solution of the equation.

[Soheil Habibian]

I did it. Thank you everyone

Answer 1

[KSSV]

You substitute the required values in the solution using subs and then call max / min.

[Soheil Habibian]

My code:

syms y(x)

Dy = diff(y);

ode = diff(y,x,2)+(c/I)*diff(y,x)+(kt/I)*y == 0;

cond1 = y(0) == 75;

cond2 = Dy(0) == 0;

conds = [cond1 cond2];

ySol(x) = dsolve(ode,conds);

g = simplify(ySol);

How can I use the subs for symfun? Thank you

[Walter Roberson]

symfun and regular sym are the same except for the indexing operation name(value).

[Soheil Habibian]

The problem is I don't know what syntax to use. Can you type it for me? thank you

[Walter Roberson]

points_of_interest = solve( diff(g, x), x );
which_sign = sign( subs( diff(g, x, x), points_of_interest ) );

After that you need to know how to determine from the sign whether you are dealing with a min or a max or an inflection point.

Answer 2

[Walter Roberson]

You take the derivative of the equation and you solve for zeros. Then you take the second derivative and check the sign at each of the zeros in order to determine whether you have a min, max, or saddle.