Error in dsolve or my error?

When I input to MATLAB:

 dsolve('D2y-4*y=2*heaviside(t-2)','y(0)=1','Dy(0)=0','t')

The response I get is:

 ans =

 exp(-2*t)/2 + exp(2*t)/2 - sign(t - 2)/4 - 1/4

However, if I use the MATLAB functions laplace and ilaplace to solve the equation, MATLAB gives me:

 ans =

 exp(-2*t)/2 + exp(2*t)/2 + (heaviside(t - 2)*exp(4 - 2*t)*(exp(2*t - 4) - 1)^2)/4

I don't think these answers are equivalent. The latter answer matches what I got with pencil and paper. So either I've done something wrong or dsolve has a logic error.

Thanks. Jason.

[Walter Roberson]

Your second version, the one you did by hand, is what Maple believes to be true as well.

[Jason Terry]

Thanks for the feedback! So perhaps this is a logic error that Mathworks should be aware of...