Hey,

I'm not really sure about the other two, but I guess Laplace transforms for 
a differential equation should be going in as a function in 
sympy/solvers/ode.py module. I'm also not really sure if I can be 
implemented inside dsolve , due to the hint priority, and the necessity of 
initial conditions but it can be surely implemented as a seperate function. 
I had mentioned it in my post below, the improvement in ODE solver one.

2. Application of laplace transform with differential equations
>

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