apply laplace transform to a differential equation, it shows subs(diff(y(t), t), t, 0) instead of D(y)(0)

syms s t Y y(t)
dEqn=diff(y(t),t,2)+diff(y(t),t)+100*y(t)==400*dirac(t-3)

dEqn =

100*y(t) + diff(y(t), t) + diff(y(t), t, t) == 400*dirac(t - 3)

LdEqn=laplace(dEqn)

LdEqn =

s*laplace(y(t), t, s) - y(0) - s*y(0) + s^2*laplace(y(t), t, s) - subs(diff(y(t), t), t, 0) + 100*laplace(y(t), t, s) == 400*exp(-3*s)

I try to use laplace transforms to solve a differential euqation. Normally D(y)(0) can be replaced using subs() function. But the result is an equation with subs() and it can't be replaced using subs(). How to deal with it?

[Andrew Tunison]

I am running into the same problem. Can you update this post if you figure it out?

[Andrew Tunison]

MATLAB only does Laplace on first order differential equations. You will need to convert your equation to a first order. I did this by creating y = dx/dt and adding it to my equation.

% Reduce to first order

% Initiate variables: here y = dx/dt
syms s t x(t) y(t) X m b k P w 

% Create equation of motion and take laplace
f1 = m*diff(y(t), t) + b*y + k*x == k*P*sin(w*t);
L1 = laplace(f1);

% Replace laplace terms
% For each derivative term you will need to multiply by another s
L1 = subs(L1, [laplace(x(t), t, s) laplace(y(t), t, s)], [X s*X+y(0)]);

% Replace IC's:
L1 = subs(L1, [x(0) y(0)], [0 0])

[Paul]

Matlab can handle 2nd and higher order differential equations

syms s t Y y(t)
dEqn=diff(y(t),t,2)+diff(y(t),t)+100*y(t)==400*dirac(t-3)

dEqn = 

LdEqn=laplace(dEqn)

LdEqn = 

To sub in a value for the initial condition of the derivative, first define

Dy(t) = diff(y(t),t);

then subs Dy(0) with its value, for example Dy(0) = 2

LdEqn = subs(LdEqn,[laplace(y(t)),y(0),Dy(0)],[Y,1,2])

LdEqn =