However this gives no solution (over-specified):
Now a counter-productive transform:
You would now have an 8th order ODE to solve.
Attempting to use the fourier transform with initial conditions yields no solution:
The following ODE has different solutions depending on whether 'pointwise'=true has been specified.
So the solution as provided does not satisfy the initial conditions in a pointwise fashion, as can be seen from
To instead enforce the conditions to be pointwise satisfied, the following can be used: