dsolve problem

Hello, I would like to use a function f in a differential equation for example f=x but get a crazy result.

syms x y f
f=x
y=dsolve('D2x=-f','x(0)=1','Dx(0)=0')

How can I put into dsolve a function f defined outside of dsolve?

Answer 1

[Teja Muppirala]

One way would be to convert f to a string:

syms x y f
f=x
y=dsolve(['D2x=-' char(f)],'x(0)=1','Dx(0)=0')

[Daniel]

Thank you Teja!

Answer 2

[Walter Roberson]

You could try

syms x y f
f=x
eqn1 = subs(sym('D2x=-f'), 'f', f);
y = dsolve(eqn1, 'x(0)=1','Dx(0)=0')

[bym]

this doesn't work:

??? Attempted to access e(1); index out of bounds because numel(e)=0.

Error in ==> sym.sym>char2sym at 415

sk = x(s(k):e(k));

Error in ==> sym.sym at 134

S = char2sym(x);

Error in ==> sym.horzcat at 17

args{k} = sym(args{k});

Error in ==> dsolve at 121

[sys_parsed, err] = feval(symengine,'mlconvertode',sym(['[' sys_str(1:end-1) ']']),x);

[Walter Roberson]

Ah, I guess it doesn't analyze syms for occurrences of D. Ummm, I will have to make up a variable for x to be related to:

If I read the documentation right,

syms x(t) f(t) t

f = x(t); %or maybe f = x;

D2x = diff(x,2);

Dx = diff(x);

dsolve( D2x == -f, x(0) == 1, Dx(0) == 0 )

Anyhow, the root of the problem is that, as usual, when you have a quoted string like 'D2x=-f', MuPAD does not have access to the value of any variable such as f that was declared at the MATLAB level. subs() is the mechanism to "import" MATLAB-level values to the MuPAD level. It looks like dsolve() interprets symbolic variables differently than it interprets strings so the more obvious subs() does not work. char() around the subs() might perhaps have worked.

[Daniel]

Thanks for trying.

Teja's code works:

syms x y f

f=x

y=dsolve(['D2x=-' char(f)],'x(0)=1','Dx(0)=0')