Help with Laplace transform method for 2nd order DE

Question

Nina 2023-4-23

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1951568-help-with-laplace-transform-method-for-2nd-order-de

回答： Star Strider 2023-4-23

I'm trying to solve the equation: y'' +2y' +y = g(t), with g(t) = { sin(t) if t < pi, 0 if t < pi }, and the intial conditons y(0) = 0 and y'(0) = 0.

Here's the code that I've tried:

 syms s t y(t) Y
g = heaviside(t)*(sin(t)) + heaviside(t - pi)*(-sin(t));
eqn = diff(y,2) + 2*diff(y) + 2*(y) == g;
lteqn = laplace(eqn, t, s);
neweqn = subs(lteqn, [laplace(y(t), t, s), y(0), subs(diff(y(t), t, 0)), [Y, 0, 0]]);
ytrans = simplify(solve(neweqn, Y));
Warning: Unable to find explicit solution. For options, see help. 
Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON
> In sym/solve (line 317) 
>> y = ilaplace(ytrans, s, t)
 
y =
 
Empty sym: 0-by-1