differential equations - Matlab does not replace symbolic function by its expression -


i have 3 symbolic functions : sigma_r, sigma_theta , sigma_z. 3 functions expressed function of 2 other symbolic functions : epsilon_r, epsilon_theta. example

sigma_r = 125021*epsilon_r + 132154*epsilon_theta

moreover epsilon_r, epsilon_theta function of symbolic function u(r) example

epsilon_r = diff(u)

i solve following differential equation :

diff(sigma_r)+(sigma_r-sigma_theta)/r+rho*w^2*r==0

actually differential equation can expressed differential equation of u(r).

i ask matlab substitute in expression of sigma_r (and sigma_theta) variable sigma_r (and sigma_theta) expressed function of u.

matlab did when solves differential equation doesn't replace sigma_theta expression of u. replaces sigma_r.

here commands:

sigma_r = subs(sigma_r) sigma_theta = subs(sigma_theta) u(r) = dsolve(diff(sigma_r)+(sigma_r-sigma_theta)/r+rho*w^2*r==0)

it solves , returns:

u(r) = (r*sigma_theta - (r^3*rho*w^2)/3)/r + c5/r

you can see sigma_theta still dependent of u.

can please me telling matlab replace sigma_theta expression in u , solve differential equation.


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