# How to solve laplace transform for ODE with initial value condition

14 次查看（过去 30 天）
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

### 回答（1 个）

Sulaymon Eshkabilov 2021-11-15
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 ]

R2020b

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