How to solve laplace transform for ODE with initial value condition

i have tried to solve this problem

with this code :

syms t y(t) Y(s) Dy0 a b y0

Dy1 = diff(y,t,1);

eqn = laplace(t*Dy1+ y == cos(t))

eqn = subs(eqn, {laplace(y(t), t, s), subs(diff(y(t), t), t, 0), y(0)},{Y(s), 0, 2})

eqn = isolate(eqn, Y)

but it did not work, i may used the code in improperr way but i am pretty sure that the prob. has an answer not as matlap programm responde that the equation has no solution..

any help i will apretiate

Answer 1

[Sulaymon Eshkabilov]

Here is the corrected code:

syms t s y(t) Y(s) 
Dy = diff(y,t); 
EQN = t*Dy+y== cos(t);
LT = laplace(EQN, t, s);
LT = subs(LT, {laplace(y(t), t, s), y(0)},{Y(0), 2})

LT = 

Y = solve(LT, Y)

Warning: Unable to find explicit solution. For options, see help.

 
Y =
 
Empty sym: 0-by-1
 

disp('Solution is: ')

Solution is: 

SOL = ilaplace(Y)

 
SOL =
 
Empty sym: 0-by-1
 

pretty(SOL)

()

% It does not have an analytical solution:
syms t y(t)
Dy = diff(y,t); 
EQN = t*Dy+y== cos(t);
SOL = dsolve(EQN, y(0)==2)

Warning: Unable to find symbolic solution.

 
SOL =
 
[ empty sym ]