second order differential Equation

Hello everyone

i have been trying to solve laplace transforms for second order differential equation: y''(t) - 6 * y'(t) + 9 * y(t) = 3 * sinh(t), y(0)=1, y'(0)=1 by Matlab to check with my hard calculation's answer which is y(t) = ((3/8) * e^t) - ((3/32) * e^-t) + ((23/32) * e^3t) - ((13/8) * t * e^3t). However it gave a warming in line 121 and i didnt really understand how to fix it properly. If anyone has idea, please let me know.

Thank you

Answer 1

[Star Strider]

The symbolic Math Toolbox no longer uses strings. That threq the warning.

For the rest:

% % y''(t) - 6 * y'(t) + 9 * y(t) = 3 * sinh(t), y(0)=1
syms s t y(t) Y(s) Dy0
eqn = diff(y,2) -6*diff(y) + 9*y == 3*sinh(t);                                              % Time-Domain Equation
Eqn = laplace(eqn)                                                                          % ‘s’-Domain Equation
Eqn = subs(Eqn,{laplace(y(t), t, s), y(0), subs(diff(y(t), t), t, 0)}, {Y(s), 1, Dy0})      % Substitute To Create Readable Expression
Eqn = simplify(Eqn, 'Steps', 250)                                                           % Simplify
Ys = isolate(Eqn, Y)                                                                        % ‘Solve’ For ‘Y(s)’

produces:

Ys =
Y(s) == -(Dy0 + s - Dy0*s^2 + 6*s^2 - s^3 - 9)/(s^4 - 6*s^3 + 8*s^2 + 6*s - 9)

that in LaTeX is:

.