Solve the following PdE Using FT?
a) u(x,t) = (1/(2π)) ∫_[0][[infinity]] (e(-iωt) / (1 + x²)) dω
b) u(x,t) = (1/π) ∫_[0][[infinity]] (sin(ωt) / (1 + x²)) dω
c) u(x,t) = (1/(2π)) ∫_[0][[infinity]] (e(-iωt) / (1 + x)) dω
d) u(x,t) = (1/π) ∫_[0][[infinity]] (e(-iωt) / (1 + x)) dω