Using fourier and laplace transform to solve PDE

PDE is type of heat equation.

Where have above reference notes?

Many book only gives an example of solving heat equation using fourier transform.

An exercise asks me to solve it for using fourier and laplace transform:

u_xx = u_t -inf < x < +inf, t >0

u(x,o) = x

u(o,t) = 0

In the heat equation, we'd take the fourier transform with respect to x for

each term in the equation. How to combine it with using fourier and laplace transform

Can anyone suggest some example and notes to me??