Use Laplace transform to solve the initial boundary value problem for the non-homogeneous transport equation:
u_(t)+(u_(x))/(1+x)=0,x>0,t>0
u(x,0)=0,x>0 u(0,t)=1,t>0
Describe so-called...
a) Exponential growth and decay processes in the context of differential equations.
b) The Laplace transform's application in solving partial differential equations.
c) Boundary value problems and their significance in mathematical modeling.
d) The Laplace transform's role in solving initial value problems for differential equations.
