substitute only first derivative in symbolic toolbox

I am considering a second order differential equation (mass - spring system), and I want to substitute the first derivative with another symbolic function.

syms x(t) v(t) m k
expr = m * diff(x, t, 2) + k * x(t) == 0;
expr2 = subs(expr, diff(x, t, 1), v(t));

Anyway, result of expr2 still containts the second derivative of x(t) and not the first derivative of v(t). Is there a way I can solve it and make it explicit?

>> expr2
expr2(t) =
m*diff(x(t), t, t) + k*x(t) == 0

[VBBV]

Try this

 %f true
    % code
%end
syms x(t) v(t) m k
expr = m * diff(x, t, 2) + k * x(t) == 0;
expr2 = subs(expr, diff(x, t, 2), diff(v,t,1)); % the old is diff(x,t,2)

Answer 1

[madhan ravi]

I remember doing vibration analysis, used to be pretty tricky:

 expr2 = subs(expr, diff(x, 2), diff(v))

[Antonio d'Aniello]

well honestly I didn't think about that. Thank you so much!