Hi,
why do you have the 2.derivative in your code? I do only find the first derivative in your attached equation. Also i think your code is already describing v(t) since you can isolate xdot. So you already have the solution for v(t).
What you can do is solve for x(t) with the condtion x(0) == 0 - not v(0):
syms x(t) b R m a g theta J alpha
% The equation like you posted it
eqn = -b*diff(x,t)*R - m*a*R + m*g*(R*sin(theta)) == (J + R^2)*alpha;
% The isolated term for v(t):
eqn = isolate(eqn, diff(x,t));
% The solution of the ode:
xSol(t) = x == dsolve(eqn,x(0)==0);
% Write the results pretty:
pretty(eqn)
pretty(xSol)
That should be what you wanted to do:
2
d alpha (R + J) + R a m - R g m sin(theta)
-- x(t) == - -----------------------------------------
dt R b
2
t (J alpha + R alpha + R a m - R g m sin(theta))
x(t) == - -------------------------------------------------
R b
Best regards
Stephan
