# Question:Problem with laplace transform

## Question:Problem with laplace transform

Maple
I convert following differential equation to the s domain: restart: with(inttrans): > DV:=diff(y(t),t\$2)+3*diff(y(t),t)+2*y(t)=diff(x(t),t): > x:=t->10*exp(-3*t): > laplace(DV,t,s); As solution I get: s^2*laplace(y(t),t,s)-D(y)(0)-s*y(0)+3*s*laplace(y(t),t,s)-3*y(0)+2*laplace(y(t),t,s) = -30/(s+3) It's not really a Maple problem but I don't understand why the right hand side of the equation is -30/(s+3) . When I transform the right hand side of the differential equation manual to the laplace domain I would do it as: diff(x(t),t) = s*X(s) = s * 10 /(s+3) That's something different from what maple gives me and it also gives me a different solution for the differential equation. Could someone tell me what I am doing wrong here? Also when I construct the transfertfunction H(s) and I multiply it with X(s) and do an inverse Laplace transformation I get another solution then when I let maple solve it with initial conditions y(0)=0 and D(y)(0)=0.
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