How can i fix this error ?

syms s t Y
LHS = laplace(diff(diff(str2sym('y(t)')))+2*diff(str2sym('y(t)')));
RHS = laplace(8*t);
newLHS = subs(LHS,'laplace(y(t),t,s)','y(0)','D(y)(0)',Y,0,0);

Error using sym/subs
Too many input arguments.

Y = solve(newLHS-RHS,Y);
y = ilaplace(Y,s,t);

Error using sym/subs

Too many input arguments.

Error in Chay_thu_nghiem (line 4)

newLHS = subs(LHS,'laplace(y(t),t,s)','y(0)','D(y)(0)',Y,0,0);

Answer 1

[Sam Chak]

@Do Son

Try this:

% to formulate ODE
syms s t y(t) Y(s) 
D1y = diff(y);
D2y = diff(D1y);
Eqn = D2y + 2*D1y == 8*t

% to obtain the transfer function
LEqn = laplace(Eqn)
LEqn = subs(LEqn, {laplace(y(t), t, s), y(0), D1y(0)}, {Y(s), 0, 0})
LEqn = isolate(LEqn, Y(s))

% to solve ODE via taking the inverse Laplace transforms of transfer function
y(t) = ilaplace(rhs(LEqn))

[Do Son]

Thanks, it really works.

[Do Son]

But can you explain why my code didn't work?

[Sam Chak]

Because subs takes a maximum of 3 arguments. Maximum 2 commas.

[Do Son]

If you could fix on my code, how would you do that?

[Sam Chak]

Hi @Do Son

I tried avoiding lot of parentheses () and a clump of characters without spacing because they make tracing your own code and debugging very unfriendly to read and troubleshoot. Start following good coding practices.

This should work now:

syms s t y(t) Y
D1y = diff(y);
D2y = diff(D1y);

% Left-hand side
LHS = laplace(D2y + 2*D1y);
LHS = subs(LHS, {laplace(y(t), t, s), y(0), D1y(0)}, {Y, 0, 0})
% Right-hand side
RHS = laplace(8*t)
% Laplace equation
LEqn = LHS - RHS == 0

Y = solve(LEqn, Y)
y = ilaplace(Y, s, t)