Using dsolve gives a different solution than Wolfram Alpha

I'm trying to solve a differential equation (1x''+8x'+16x=50*e^(-t)*unit step(t),x(0)=0,x'(0)=0) using dsolve:

    dsolve('1*D2x + 8*Dx + 16*x == 50*exp(-t)*heaviside(t)','x(0) == 0', 'Dx(0) == 0')

and it returns:

    -Inf*sign(t)

Obviously, trying to eval is going to give a pretty meaningless result. So I decided to throwing it into Wolfram Alpha:

    {1 x''[t] + 8 x'[t] + 16 x[t] == (50 UnitStep[t])/E^t, x[0] == 0, x'[0] == 0}

where it returned:

     {x[t] == (50 (-1 + E^(3 t) - 3 t) UnitStep[t])/(9 E^(4 t))}

Am I not using heaviside correctly? Is there something simple I'm missing? I have no idea where to start debugging the problem, because it's just a built in function.

[@Johannes]

I found a similar problem from another user.

http://www.mathworks.com/matlabcentral/answers/155088-how-can-i-solve-a-differential-equation-including-the-heaviside-function-in-matlab-r2014a

In my opinion you could contact the tech. support of the mathworks to clarify your issue.

Best regards, Johannes

[light_dark]

So I tried the second method where I use a constant instead of the heaviside function in dsolve and it appears to give the correct solution, but when I use subs to replace the constant with the heaviside function, I end up getting what appears to be an array of solutions (first element is 0, the rest all look to the solution), with the length of the heaviside function. Why does this happen? I'm thinking that it's substituting at each value of the heaviside function.

[@Johannes]

I tried the second method in R2015b too. I don't get an array of solutions. I get a symbolic variable which contains the substituted solution. Plotting this solution leads to the same plot as wolfram alpha delivers. Not sure if i misunderstand you.

Best regards,

Johannes

[Walter Roberson]

I would try recoding in terms of diff() instead of replying on the D parser. The initial condition D(0) might require some investigation to recode though.