Laplace transform not getting Value

I tried to solve lapalce but not getting the value (Xs). Find the code below, Is there any issues in the code?

syms x(t) Xs
eqn  = diff(x,t,2)+2*diff(x,t)+26*x(t) == 10*cos(t)*(heaviside(t-pi));
eqnLT = laplace(eqn)

eqnLT = 

eqnLT = subs(eqnLT,laplace(x(t)), Xs);
eqnLT = subs(eqnLT, {x(0), diff(x(t), t, 0)}, {1/2,1});
Xs = solve(eqnLT, Xs)

Xs = 

Answer 1

[Star Strider]

I do not see any specific problems.

syms x(t) Xs s 
eqn  = diff(x,t,2)+2*diff(x,t)+26*x(t) == 10*cos(t)*(heaviside(t-pi));
eqnLT = laplace(eqn)

eqnLT = 

eqnLT = subs(eqnLT,laplace(x(t)), Xs);
eqnLT = subs(eqnLT, {x(0), diff(x(t), t, 0)}, {1/2,1})

eqnLT = 

Xs = isolate(eqnLT, Xs)

Xs = 

X(s) = rhs(Xs)

X(s) = 

Perhaps the isolate function will do what you want.

.

[BEENA BASHEER]

Need to plot using below getting error:" Input must be a function handle or symbolic function." while using isolate

figure(1)
fplot(Xs, [-10 100])

[Star Strider]

The equation needs to be set up correctly, and here it is not.

There is a typographical error in:

eqnLT = subs(eqnLT, {x(0), diff(x(t), t, 0)}, {1/2,1})

since it should be:

eqnLT = subs(eqnLT, {x(0), subs(diff(x(t), t), t, 0)}, {1/2,1});

and with that change:

syms x(t) Xs s X(s) 
eqn  = diff(x,t,2)+2*diff(x,t)+26*x(t) == 10*cos(t)*(heaviside(t-pi));
eqnLT =  laplace(eqn);
eqnLT = subs(eqnLT,laplace(x(t)), X(s));
eqnLT = subs(eqnLT, {x(0), subs(diff(x(t), t), t, 0)}, {1/2,1});
eqnLT = isolate(eqnLT, X(s))

eqnLT = 

It does not eimplify further. (I checked.)

.

[BEENA BASHEER]

Wow! It helps me a lot! Thanks!

[Star Strider]

As always, my pleasure!

.

Answer 2

[Walter Roberson]

syms x(t) Xs
eqn  = diff(x,t,2)+2*diff(x,t)+26*x(t) == 10*cos(t)*(heaviside(t-pi));
eqnLT = laplace(eqn)

eqnLT = 

eqnLT = subs(eqnLT,laplace(x(t)), Xs);
dx = diff(x,t);
eqnLT = subs(eqnLT, {x(0), dx(0)}, {1/2,1});
Xs = solve(eqnLT, Xs)

Xs = 

[Sarthak]

%write a matlab code to find the solution of following differential
%equation using Laplace transform method
%d^2y/dx^2-3dy/dx+2y=sinx, y(0)=2, y'(0)=2